Yes! You finally asked a random question that I can answer! The easy answer to your question is to say, “South Americans looked to Great Britain with its mature constitutional monarchy that balanced authoritarianism with democracy, Europe with its Enlightenment ideas, and the United States as a model New World republic.” If I were to give you this response, it is technically right but far too simplistic. South American nation builders weren’t simply trying to copy a government but to mold a whole new society that seemed to be careening dangerously toward disaster. They looked to other parts of the world for ideas on government, but they were more concerned with larger social questions of which the form and structure of government was merely a small part.

Okay so first, contrary to popular belief, 18th century americanos were not cut off from the Enlightenment prior to Independence just because communication was slow and trade was discouraged. Recent Atlantic scholarship had consistently shown that the “closed” empires were quite porous. Educated, elite americanos regularly read Locke and Rousseau. They talked about liberty, equality, and fraternity with traders, sailors, and travellers. They studied British limited monarchy. They were familiar with popular sovereignty and the social contract. They heard about the salons of Paris. Many americanos actually travelled to Europe and experienced this first hand. Far from receiving a “bad political education” like many historians have described, many elites on both sides of the Atlantic played around with these ideas and implemented them in the colonies. There was a general modernizing spirit in the latter half of the 18th century permeating the Spanish Empire.

These ideas weren’t powerful enough to spark intense independence movements. For example, Francisco de Miranda failed to start a revolution in Venezuela in 1806 when he landed an invasion force. Miranda was heavily influenced by the British constitutional monarchy and Enlightenment ideals. He participated in the French Revolution, fund raised in Britain, and spent time in the United States recruiting norteamericanos to join the invasion in the spirit of liberty and freedom. However, few in South America were interested in joining Miranda’s cause. The expedition was defeated, and Miranda died in a Spanish jail.

Actually though, Enlightenment ideas weren’t as contrary to the Spanish imperial system as we might think. There were lengthy traditions of “people power” in medieval Iberian legal traditions. For instance, José Chiaramonte has written several books and articles about various legal currents that impacted early 19th century thinkers. Off the top of my head, I am reminded of an article he wrote on Spanish natural law, which (and I am simplifying greatly) was similar to natural rights. At the same time, there was the tradition that colonial leaders could disregard royal orders if the people objected too vigorously or a decree was otherwise unable to be implemented in the local context. Famously, the administrators “obedecen pero no cumplen” (Obey but do not comply). And most importantly for early independence thinkers, when the king was unable to carry out his leadership role, power resorted back to locals to rule in the king’s place. When Napoleon invaded, these local councils were the first ones to face the question of new government, but most of them didn’t actually want to become independent. Only a miniscule few wanted to break with Spain completely. At first, most americanos remained loyal to the Spanish monarchy, though they sought economic changes. They also generally wanted to elevate the colonies to the same status as other Iberian kingdoms.

As violence broke out, spread, and wore on, the juntas generally took decidedly authoritarian stances on governing because there really were many enemies who really did intend to destroy their new reforms. It eventually became evident to many of these leaders that remaining a part of the Spanish Empire would not achieve the social, economic, and political goals that they found most pressing. It is at this point that they declared independence.

So who were they looking to for guidance? Their speeches and constitutions were filled with the usual Enlightenment lingo on citizenship, “the people,” freedom, and “the nation.” But they combined the grandiose Enlightenment ideas with their own local situation and flavored it with the legal traditions within their legal system.

As the revolutionary era took hold, the americano elites looked around and realized that their newly independent states were different than anywhere else in the world. Unlike Europe, they did not have long monarchist traditions. They also viewed themselves as culturally behind Europe. Unlike the United States, the leaders believed their citizens were more backwards, uneducated, and barbaric. Indigenous populations either didn’t care about the new state or might gain too much power before they were ready for it, which would destroy the new state in Haitian style or Túpac Aramu style violence. Unlike the United States, they saw their society with a vast split between poor indigenous populations and the white, rich elites in the metropolis. In their view, the United States did not have a disparity as substantial as South America’s.

Early independence leaders then looked to meld Enlightenment and Revolutionary ideas to the South American context. This context is why you see Bolívar implement a constitution where the president serves for life. It is also why elite americanos around the continent erected substantial barriers to political participation including wealth requirements, literacy requirements, land requirements, and job requirements to vote in elections.

But these initial conceptions of government ultimately failed, and the civil wars ground on and on. Many began to believe that the reason their republican governments had failed to achieve order was because of irreconcilable cultural differences. Throughout the middle part of the 1800s, South American elite leaders believed that Europe was the most modern and culturally advanced place in the world. To create functioning governments, the goal became to copy European culture and to encourage as much European immigration as possible. Domingo F. Sarmiento of Argentina believed they needed to transplant the roots of a European plant cutting to grow a more civilized Argentine society. Juan Bautista Alberdi famously said “Gobernar es popular” (to govern is to populate). To mid century 19th century leaders, Europe was the most influential place to look to because their cultural achievements had ensured that they became the most advanced, powerful, and economically vibrant place on Earth. The inherent backwardness of the indigenous populations held back the South American nations and their governments.

However, other South Americans weren’t on board with this take on government. James Sanders points out in his book The Vanguard of the Atlantic World, that by the mid 1800s, most democratic movements in Europe had failed. The United States wasn’t much better. Their society exhibited slavery, racism, and aggressive expansion. Sanders argues that to many americanos, Latin America was the most advanced place for freedom and democracy anywhere in the world.

The middle of the 1800s also saw Latin America become much more suspicious of the United States. Sanders writes in his book that early on, most Latin Americans had viewed the United States as a “sister republic” that was traveling down the same road (and encountering many of the same challenges) as they were, but with increasing US aggression against Latin America, many began to think differently about the US. The Mexican-American War, significant racial discrimination, belittling political attitudes, and the Spanish-American War all changed the view of the US from a peer to a dangerous neighbor.

So where were americanos looking to for inspiration and influence? They looked to Europe for their Enlightenment ideals and later their cultural values. They looked to the United States as a sister New World republic. But they also looked to their own legal traditions bequeathed by Spain and the unique context that each new state had to face. The process of state formation was slow, and the nations that resulted formed over time. They were the result of the experimentation with different inspirations, influences, and contexts rather than the intended destination at the outset of the 19th century.

Sources:

• The Vanguard of the Atlantic World: Creating Modernity, Nation, and Democracy in Nineteenth Century Latin America by James E. Sanders
• The Invention of Argentina by Nicolas Shumway
• A History of Chile by Simon Collier and William Sater
• Chile: The Making of a Republic by Simon Collier
• Independence in Spanish America by Jay Kinsbruner
• Latin American Independence: An Anthology of Sources edited by Chasteen and Chambers
• Beneath the United States: A History of US Policy toward the United States by Lars Schoultz

Of course I'm happy to participate in a social experiment with the goal of accumulating all human knowledge, online. Seriously though, it's an interesting question. As I dealt with international influences on Simón Bolívar for my oral examination I'll focus mostly on him in my answer, as (probably) the most famous of the libertadors today, and founder of quite a few Latin American nations. I'll try and extrapolate some more general trends regarding your question from his example.

As a heads up, this will get quite a bit longer. I focus on three main parts: precursors to the Latin American independence movements; international influences (incl. US/British/French) on Spanish American thinkers, esp. Bolívar; and lastly these influences' local adaptation, as well as continuing colonial influences.

Precursors to independence

In contrast to the wide-spread Bolívar myth (highlighting solely the „liberator's“ importance), it should be highlighted that Bolívar and his collaborators built on the work of various precursors and teachers. These constitute examples of attempts at implementing European and Northern American models of governance in Spanish America already at the turn of the century. However, the later wars of independence profited from political upheavals in Spain and South America. My focus in this part will be on the late 18th an very ealry 19th c.

Precursors:
Limited Indian revolts took place in response to the burdens of tribute and forced labor quotas, especially in connection with the repartamiento system. Political revolts included one known after its leaders as the Tres Antonios in Chile (1780) – it called for one of the most democratic agendas at the time. Social rebellions took place as well: More than 60 such revolts started in the 1770s alone in the Andes. However, they rarely moved beyond their place of origin and did not plan to topple the colonial regimes. A more extreme case was the famous rebellion of Túpac Amaru II that began in 1780. It had serious social overtones as Túpac had been radicalized by the system of forced labor and forced sale of goods to Indians, as well as by tax increases. The fact that indigenous people and members of other (non-Spanish) castas fought on the rebel's side might have alarmed creoles that a war against the Spanish might unleash an indigenous uprising. Another form of revolt was civil protest. The independence movement can be seen as a direct result of the logic and method (if not the demands) of these protests. They sometimes escalated into open revolt as well, and were founded on traditional Spanish political theory: That is the elite's belief in virtual rather than actual representation, in that they were governing on behalf of society. Examples of civil protest include the Quito rebellion and the rising of the comuneros (near Bogota), which had creole, mestizo and indigenous participation.

„Teachers“:
Teachers is not the perfect term here, I'm looking at earlier thinkers who influenced Bolívar and others. One famous example, Simón Rodríguez, was actually Bolívars childhood teacher though, and participated in his independence campaigns as an educator. Rodriguez' influence on Bolívar is hard to gauge, as they held increasingly divergent opinions in Bolívar's later life. Rodríguez had a more radical (/ambitious) plan than most of his contemporaries – he advocated for a Spanish American social revolution to accompany the military revolution. According to him, the education of a generation of students would create a democratic society from the ground up. This was quite different from the 'top-down'-approach taken by most leaders in the post-independance period. He looked to typographic innovations as attempts to circumvent the divisions between lettered oral culture, allowing not-learned readers a clearer approach to his arguments. Rodríguez was a strong proponent of American originality: According to Ronald Briggs he “had seen the fruits of Enlightenment and found them wanting”. Thus in his teachings he took into account the poor and orphaned; and called for a transcendence of racial identity through the elevation of mestizaje - both uncommon arguments at the time to say the least (Rodríguez is a pretty fascinating figure). Lastly, he wanted to learn from European political mistakes and copy the successes.

Another interesting precursor was Francisco de Miranda. He had a grand design for Spanish America as an autonomous, monarchical empire. In 1806 Miranda attempted a failed invasion at Coro, Venezuela. In the following he sent word from London to Venezuela's Creoles to assume control of the provinces (in mid 1808) – Caracas' first autonomous junta was formed in 1810.
As a dictator during Venezuela's short-lived first independence Miranda held plans for a Pan American Union (not that dissimiliar from Bolívar's later plans). Bolívar at that point shared much of Miranda's perspective: Both were in favor of British support, the British political model, perceived the American Continent as a whole, and both saw the importance of public relations with England and Europe; although it should be added that Bolívar was already more pragmatic than Miranda and saw him as idealistic. Nonetheless, I tried to show two major influences on Bolívar's later policies with Rodríguez' and Miranda's influence. And more generally that there were many precursors to the independence movement, not only in earlier leaders (there were many more of course), but also regarding earlier revolts and forms of protest.

In light of your question I'll simply skip the independence wars themselves and come to the next point. One development still to be highlighted regarding the wars are the siginificant upheavals in the early 19th c. which influenced the independence movements' ultimate successes, and aided them in comparison to their precursors. Upheavals include the Seven Years' War and Napoleons' invasion of Spain and capture of its monarch; and the Spanish pince/later king Ferdinand resorting to coercive measures (sending armies) to squeeze revenues from merchants around the empire. This meant that the old loyalist coalition, held together with the promise of a measure of home-rule and regal loyalism, was smashed and that the new coalition, of which many had preferred home-rule in empire, opted for secession.