I don't think that you will be able to terminate your trip at Bangkok, if your ticket only shows BR 62 VIE-TPE. Bangkok is only a technical stop, even BR has the fifth freedom rights. Unless you are able to ticket VIE-BKK as one flight (BR 62), and then BKK to TPE on another flight (BR 202 or BR 212 or BR 68 or BR 76), I really doubt the agents at VIE can check your bag only to Bangkok.

If you only have a carry-on, you can technically just leave at BKK during the stop since all passengers have to deplane anyway (but it will be courteous to notify the ground staff that you are terminating at BKK, so they won't delay the flight looking for you at the airport. You don't want some poor ground staffs running around BKK looking for you.) However, if you want to terminate your trip at TPE, you should have no issues short-checking your bag to TPE.

That's just my two cents.

Carfield