This thread has current info on getting a visa in Hong Kong: forumosa.com/taiwan/viewtopi … a#p1573835
US citizens can not get a China visa in Taiwan. The passport must be sent to another location and there are travel agents in Taiwan that will do it for you… for a price.
This thread has some info on getting visa in Taiwan: forumosa.com/taiwan/viewtopi … 7&t=125242