The Thai embassy in Taiwan has not adopted evisa yet, so you would have to apply in person. But the requirements for the tourist visa shows a requirement to be a citizen of Taiwan. This is a very common requirement of Thai embassies in that region of the world (same in Korea and in Japan) so I don't think you can apply for any Thai visa in Taiwan. You can double check with the Thai embassy though, but the website shows you have to be a resident.
Requirement number 3: Original Taiwan identification card OR Taiwan resident certificate with ONE photocopy
***************************************************************************************
*****
a