Getting this in writing was a bit of a pain, but the Taipei tax office has confirmed that foreigners who are tax resident in Taiwan can (and should) have their “Tax Jurisdiction Code” box filled out as “TW”:
If an individual who complies with the provisions of Article 7, Paragraph 2 of the Income Tax Act is considered a tax resident of the Republic of China. The “Tax Jurisdiction Code” of the withholding and non-withholding tax statement should be based on the individual’s actual country or region of residence during the taxable year, not the individual’s nationality. Therefore, if an individual with U.K. nationality qualifies as a tax resident of the Republic of China, the “Tax Jurisdiction Code” should be filled in as “TW”.
First response:
“Please say it more clearly.” 
Second response:
I received another withholding statement from Richart/Taishin last week again misdeclaring me as “GB”, two weeks after I visited the branch with my entry/exit record and tax residency certificate and explained again that I’m only tax-resident in Taiwan (third time now, not including the four times they asked me when signing up for the Richart account). The branch manager insisted that this is referring to nationality and should remain as “GB”, but they said they’d call me back (they haven’t, despite it being almost three weeks later). The most recent tax withholding statement also answers “no” to the 183-day question.
Now I’ve got the above from NTBT, I’ll be e-mailing Taishin again complaining that they haven’t called me back again, telling them that the branch manager was wrong, and saying that if they send me one more incorrect tax withholding statement misdeclaring my tax residency (for October, due in late November I guess) I’ll be reporting them to the tax office and FSC. 
I believe the former (or MOF, not sure) issues fines for these being completed incorrectly.