I had a paper on Insurgency in North East India in university so I'll try to answer you to the best of my abilities.

As you said, separatism or state rights are the primary motive of all these groups. The sentiment arises from the perceived notion that mainland India and the central government don't give adequate importance or attention to the issues of the North East. Which is sadly true to varying degrees depending on the state. NE states are underdeveloped compared to the mainland, people from the NE are discriminated against or stereotyped by mainland Indians. There are also a huge amount of tribes in the NE, all of them vying against each other for influence and recognition so nationalist ideology has many takers. The lack of development causes unemployment, a rich source to recruit insurgents from.

Even from a historical standpoint, the NE has been neglected by historians and other academics and even politicians. When India was on the verge of independence and lines were being drawn to decide India and Pakistan, the Congress famously didn't want Assam and made little effort to prevent it from becoming Pakistani territory. Assam had a high percentage of Muslims in 1945-46 owing to the machinations of a man named Saadulla who was the minister governing Assam during the Quit India Movement when the Congress got outlawed and its leaders jailed. Saadulla was a knighted British stooge, a leading lieutenant of Jinnah and a member of the Drafting Committee of the Indian Constitution. During WW2, Saadulla initiated a food growing programme called Grow More Food to help the British war effort and clandestinely shape Assam for assimilation into Pakistan. Do note that the other NE states didn't exist during this period other than Arunachal Pradesh, then called NEFA. Citing agricultural labour requirements, he brought millions of labourers from the Sylhet, Dacca and Mymensingh districts of current Bangladesh who were Muslim, driving up the Muslim population percentage. He made preparations for their settlement and scattered them all over the forest tracts of the state infringing upon traditional tribal territories and driving them out. It took a desperate eviction campaign by local Congress leader Gopinath Bardoloi to forcibly drive down the percentage and drive the temporary labourers back where they came from, thus saving Assam from becoming a part of East Pakistan. He had no help or support from his Congress colleagues from the mainland and had to personally mobilise Assamese society to help drive the labourers out. This is seen as a huge betrayal from the Congress by the various people of the North East.

In this kind of political environment, its easy to mobilize unemployed youth disillusioned by the Indian government headed by Congress leaders. The prospect of protecting one's culture and a steady source of income was appealing, not helped by the fact that their arguments did have some merit to them.

Just intent won't form an insurgent group, you'd need funding, weapons and training. So where do these separatist groups get their funding from? Mainly China and Pakistan. The process of starting a separatist terror group is not unlike an unholy Shark Tank episode. An interview with Aurobindo Rajkhowa, one of the founders of the Assamese separatist group ULFA, reveals that Pakistani ISI infiltrators move freely within the country and come to know of separatist sentiments through through the local grapevine. Then the ISI agent contacts the would-be leaders and after assessing the seriousness of intent, issues fake identification and smuggles them to Islamabad or Karachi via other countries. There, they meet with a senior ISI agent and have to pitch their terror group idea to them such as goals, recruitment expectations, budgetary requirements, ways in which the Indian Union would be undermined by their activities etc. After receiving funding, a recruitment drive is held in the rural parts and then the recruits are shipped off to Myanmar where they get guerrilla training by the rebels such as the Karens who get paid for their training (this is why India maintains cordial relations with the junta). Many of these insurgent camps are situated in Myanmar, Bangladesh and China where its difficult, if not impossible for Indian anti-terror operations to get permission to operate.

Indian response to these groups usually start off with disproportionate use of force by the army and various human rights offences such as displacement of people, burning down of villages, imposition of Armed Forces Special Powers Act (AFSPA) etc. This achieves literally nothing and alienates the society against the army and by extension India even though most of them weren't separatists before. Now the separatists have some sympathy and support of the local community and are able to operate with more impunity. The government has no option but to try repair bridges, which means giving into the demands of the insurgents. Since separation from India isn't an option, the next best thing is the creation of a new state carved out from Assam. Mizoram is an example of such a state.

A good book you can read regarding this subject is Strangers of the Mist by Sanjay Hazarika.