I see that Speedoo1 mentioned weather in Taiwan is perfect in October and November. Doesn't the Taipei Gay Pride Parade take place around this time? Photos on other forums make it look a really fun day with tens of thousands of great looking guys. I assume they are Taiwanese although I know it has become quite a tourist attraction for gays from around the region.
Taipei Pride is always the last weekend in Oct. This year it is 31 Oct. But as a foreigner/from outside TW you will have no chance of entering TW by next month.
Formosa/Taipei Pride is a blast with handsome fit/muscle Asian guys from all over Asia - a lot from HK, SG, Korea etc flying into TW for the weekend. Most guys are into Asian though. Book accommodation ahead as the city is very busy during Pride weekend. Outdoor bars at Red Square will be extremely crowded Friday and Saturday nights. This year I assume that the Pride will be much smaller as visitors will be far less.