Democratization would happen faster,
Not quite. Democratization really kicked off in Taiwan after a series of scandals, including when
a leading Taiwanese critic of the GMD
got assassinated by Triads inside the United States. It proved to be such a huge scandal in both Taiwan and the US - particularly as it turned out that the Triad gang involved had strong ties with the GMD, leading some to suspect the GMD ordered the hit, and in effect the US humiliated the ROC into cleaning up its act as atonement - that the localization strategy Jiang Jingguo took had to be accelerated, and hence the onset of democratization.
Having said all that, I'll take a stab at the OP. In effect, if we're having Jiang Jingguo (蔣經國) die shortly after Jiang Jieshi's death, that would mean that in 1978 we'd have Jiang Weiguo (蔣緯國)'s election instead. There are some things I'd think would be similar between Jingguo IOTL and Weiguo ITTL, namely the completion of
Ten Major Construction Projects and the launch of the Twelve New Development Projects, hence contributing to Taiwan's economic modernization. I don't see Weiguo lifting martial law and trying to promote more Taiwanese into government service, and the pro-democratic opposition and the Tangwai movement would continue to face harrassment (while still determined to bring democracy to Taiwan). Due to his background, Weiguo would probably focus more attention on the ROC Armed Forces and all that (even though he'd have to resign from the Army first before becoming President); at the same time, China's changing under Deng Xiaoping (though usually it was Deng trying to catch up with everyone else). For the most part I don't see relations with the Mainland changing too too much, however if Hu Yaobang and Zhao Ziyang (and people in the CCP like them) were able to prevail a lot more and change China towards being a Singapore writ large, that I think would be comfortable enough for Jiang to consider calling for a truce with the PRC and thus lead towards (re)unification over the objections of the Taiwanese people. The Taiwanese will have other ideas and would want both democratization to happen faster and to keep as much distance with the Mainland as possible, giving the Pan-Green camp more momentum ITTL. I don't think Weiguo's Nazi past would harm him in China and a certain section of Taiwanese society too much, but if Henry Liu's assassination by the Bamboo Union still goes ahead as per OTL then it would prove embarrassing in the US and Taiwan that a Taiwanese leader was once part of the Wehrmacht, permanently sullying the Jiang family name and giving new lease on life to the pan-Green camp and the Tangwai movement, along with additional momentum from the push towards (re)unification as a way for Jiang to save his face (in which case the Tangwai movement would be a reaction from the Taiwanese people asking the Government to stop). In this case I could eventually see the pro-democratic camps in both HK and Taiwan link up, with consequences even I can't foresee.