It turns out we’ve been wrong about this. A Taishin employee corrected me today when I said my tax withholding certificates should read not “GB” for the UK but rather “ZZ” for Taiwan, like the first one I received did.
According to him, “ZZ” actually meant “we weren’t sure”, which is confirmed by this file from the Kaohsiung tax bureau listing it as meaning “other”.
Taiwan, unsurprisingly, is “TW”. I’d always kind of wondered why it wasn’t, but I interpreted the use of “ZZ” as something like “question invalid, no other tax residencies”. I should really have checked this before though. Oops. 
On the plus side, I must have mentioned this to almost a dozen bank employees by now, and he was the first one to correct me. He was probably the first one who knew. 
Coincidentally, Mega Bank told me this morning they don’t need to write anything there, can just leave it blank. 