I'm unsure if a comment like this is allowed, but it would be interesting to have the premise of the question addressed as well--is it accurate to describe these countries as being "brutal dictatorships?"

Disclaimer: I am not a professional historian and all the information here is from what I have learned from high school and otherwise. If this comment does not meet the standards of this subreddit, then please notify me mods. This answer focuses on Taiwan only.

Martial Law Era

In order to understand the context of Taiwan's dictatorship in the 1980s, we will have to wind back the clock to 1949. (My answer focuses more on events after 1949 so the 228 incident would not be elaborated).

The Nationalist regime (Kuomintang) has lost control of northern China by the start of 1949. Then Taiwan's governor Chen Cheng announced on 19 May of province-wide Martial Law for Taiwan (including the Pescadores islands). Coming along with Martial Law would be the banning of all other political parties (党禁) and censorship of media (报禁). Any political opposition to KMT rule would have to come from outside the party, so called Tangwai movement (党外运动). No new newspapers were allowed to be established. Although even under the so called "White Terror" that lasted to the end of the 1980s, democratic activists could still run for offices of prefecture mayors, city mayors and legislators for Taiwan's provincial parliament, but they have to run as independents.

Some important political incidents/milestones (certainly not all) in Taiwan's democratic movement until the 80s:

Lei Chen incident

Before the end of the Chinese civil war some liberal intellectuals in China (eg. Lei Chen, Hu Shih) had planned to establish an anticommunist magazine, Free China (自由中国) to counter communist ideology. When the mainland fell to the advancing communist army, Free China was therefore only published in Taiwan. Chiang Kai-Shek had tolerated criticisms from Free China about his dictatorial rule since he had a relatively amicable relationship with Hu Shih. But that attitude changed in 1960 when Chen planned to established a new political party. Chen also called for opposition to Chiang running as President for the third term (it was unconstitutional). The political party Chen envisioned for failed to materialise. He was instead arrested by September that year and sentenced to ten years in prison.

Zhongli incident

Local elections were held in Taiwan during 1977 including for the mayors of Taoyuan prefecture. At 19 November voters in Zhongli District of Taoyuan believed that the KMT regime had committed voting fraud in the election and protested against the abuse of power by the government. The protests evetually escalated to the point where the local police station was surrounded and burned down. Eventually the police was called in to confront the protests and restore order, during which several youths were shot dead with live ammunition. The heavily censored Taiwanese media did not give significant coverage about the incident until several days later. Ironically, the independent Tangwai candidate won the election for Taoyuan's mayor anyway. This incident was the first time street protests appeared in Taiwan since 1947.

Formosa Magazine incident

One of the strategy for Taiwan's democracy activists to fight the KMT was to create publications (basically books, magazines, media) that were spread underground to circumvent KMT censorship. One of the more influential of such publications is the Formosa Magazine. On 10 December 1979 (international human rights day), demonstrations were organised by members of the Magazine publication and opposition politicians outside of the Magazine HQ in Kaoshiung City, which devolved into the largest confrontation between the protestors and the police during the Martial Law era (just imagine the ongoing HK protests but taking place in 1970s Taiwan). The protests were evetually suppressed by the police. Eight core members of the magazine were arrested and charged with "treason".

Assassination of Henry Liu

The assassination of Henry Liu on August 1984, a well-known Taiwanese jounalist, author would see US-Taiwan relations go to rock bottom. He was the author of Biography of Chiang Ching Kuo (son of Chiang Kai Shek, President of ROC 1978-1988). His book had displeased the KMT leadership and Taiwan's government had tried to ban any independent media to publish Henry's content (he wrote a lot of articles analysing/critiqing Taiwan's politics as well). The US government was very unhappy with the murder since Henry was also an American citizen. Not only does KMT's reputation decline because of Henry's death (and other dissidents' assassinations over the decades), it would also claim the political future of Chiang Hsiao-wu, grandson of Chiang Kai Shek who was groomed to take power after Chiang Ching Kuo (he was 34 when he entered Taiwan's "National Security Council" in 1979). Since he was implicated in the assassination (although it is disputed who gave the order).

Establishment of the Democratic Progressive Party (DPP)

By the mid 1980s the Tangwai movement had gradually coalesced into a more coordinated political force to contest elections for the Legislative Yuan and the National Assembly. When opposition figures gathered at Taipei's Grand Hotel on 28 September, 1986, one of the opposition figures, Ju Gau-jeng, advocated for the establishment of a party at once. His original quote (in Mandarin):

我坚决反对，民主运动发展到这个阶段，大家还坐在那儿讨论“组党筹备委员会”。当年雷震还在筹组政党阶段，就已经“鸡仔鸟仔抓到没半只”（闽南俗话，比喻“一网打尽”）。组党靠决心与勇气，我正式建议：今天，现在就宣布组党！

Rough translation: Ju asked for the delegates who attended the meeting to form a political party *today*, in order to avoid the fate of Lei Chen in the 1960s.

Many hardliners in the KMT regime (such as then Chief of General Staff Hau Pei Tsun) demanded the newly founded DPP to be banned when they heard of the news. But Chiang allowed it to exist instead. He commented that:

The times are changing, the trends are changing, the environment is changing.

Chiang Ching Kuo was not necessarily a benevolent dictator just acting from his good faith. Since he has ample reasons to not crush the DPP.

First reason was the fact the KMT regime is not an indigenous government (it fled from the mainland) and the army's composition was leaning more heavily towards Taiwan's native population by the mid 1980s. His administration might not have survived if the KMT encounter another insurrection like the Formosa Magazine incident. Who would guarantee the army would not turn against Chiang and his cadre of mainland Chinese senior officers?

Second reason was the United States' attitude. The State Department was not at all happy with Chiang's human rights records in Taiwan, an array of unsolved political murders/assassination certainly tainted the international image of the KMT. Not to mention the increasing influence of the communist government on the world stage. Chiang could not afford to offend the Americans too much if he wanted to survive in a changing world order.

I'm going to highlight a wider geopolitical point that hasn't been mentioned here:

China affirmatively switched sides in the Cold War with the 1979 signing of the Joint Communiqué. Arms sales and military cooperation began the same year.

The main impact is that US allies along the Chinese periphery were no longer so critical, and American support was no longer guaranteed. At the same time, with the start of Evil Empire/National Endowment for Democracy rhetoric in the US with regards to Eastern Europe from 1983 onwards, these regimes were both more costly and less useful to support.

The impact of this shift was not felt first in Korea or in Taiwan, but in the Philippines: in 1986, Ferdinand Marcos called an election after years of heavy American media pressure. The media, in particular the New York Times, would be heavily critical of Marcos's misuse of American aid funding and pitched Marcos as endangering US military interests by perpetuating conditions conducive to armed revolution. Marcos sought to present himself to the Americans as the only alternative to communist dictatorship, but the US State Department under Reagan pursued a "third force" strategy of propping up moderate reformists who would be credible leaders of an urban protest movement and win democratic elections. Michael Armacost, a former ambassador to the Philllppines who had now been promoted to State, described the strategy as "to encourage the democratic forces of the center, then consolidate control by the middle [classes] and also win away the soft support of the [communists] [by]... cueing in initiatives pushed by the business class and the middle classes... [who] are the ultimate arbiter of succession".

Likewise, in Korea, we can see the evolution in US policy by comparing the US response to Gwangju in 1979 and to the protests in 1987. When Chun Doo-Hwan first declared martial law in 1980, the US response was to issue a statement. In contrast, in June 1987, when Chun sought to deploy troops to the campuses, the US ambassador James Lilley informed Chun that to do so would threaten the US-ROK alliance ("This is the American position. The [US military] command is with me. I speak for all of the United States."). By the evening the same day, Chun suspended the mobilization.