There will be a government in exile (not in Taiwan) of Taiwan (Aka ROC) which is supported overtlyt by the US
Counts
US provides security and resources to escaped taiwanese government officials after an invasion by the PRC and those officials and the US claim they are the rightful government or should be restored to control of the island of Taiwan.
A single individual is allowed to live and speak in the US or other western country which democratic party think tanks support as a better leader in government on the island of Taiwan, even though republican leadership opposes him, and even if he has never held political office in Taiwan
A natural disaster or military coup strikes tw and the existing leadership flees to Japan but claims to rule, even if on the island there are other group(s) who claim they are in charge.
Taiwan transitions to dictatorship or other type of government and there emerges a democratic group of taiwanese either former leaders or new on the US, which the US supports as the rightful government
Doesn't count
Individual in the US claims to be the rightful leader of Taiwan but unmentioned by the US gov or official apparatus
China supports the idea that other people should lead Taiwan for example PRC citizens, and that the government of Taiwan at present 2023 is not legitimate