I found a series of posts for ABT children about how to get a ROC passport and then citizenship.
The first post starts with a flow chart to help you determine if you can get an ROC passport through your parents.
These are the supporting documents you need:
Supporting documentation to confirm that the applicant is a legitimate child of a Taiwanese parent
- Original (if available) and copy of Taiwanese household registration booklet or Taiwanese national identity card of at least one parent
- Original (if available) and copy of parents’ marriage certificate: if issued outside of Taiwan, you must have it translated into Chinese (DIY is okay): send both to TECO to verify (US$30**)
- Original (if available) and copy of your original birth certificate and Chinese translation (DIY is okay): send both to TECO to verify (US$30**)
She includes a link to a post written by someone who is British. https://jargoned.com/travel/becoming-taiwanese-if-your-mother-is-taiwanese/01/2020/
After you get your passport, you enter Taiwan and follow additional steps to become a citizen, (which will give you the right to work and to receive health insurance I believe).
She recommends that you get your FBI history before you leave the U.S.
" Prior to moving to Taiwan, I would recommend that you request an Identity History Summary (IHS) from the FBI. You don’t actually need to produce it until you reach the second step, but the FBI takes US$18 and 12-24 weeks to process these requests. Be aware that the IHS is only valid for six months from the date of issue, so don’t get it too much earlier than when you plan to enter Taiwan with your no-ID passport."
Here is the FBI form https://forms.fbi.gov/identity-history-summary-checks-review/q384893984839334.pdf
You need to get your fingerprints taken. file:///I:/2020%20documents%20on%20j%20drive/taiwan%202020/TECO/household%20registration%20transcript%20english/temp2.pdf
You will also need original paper proof of your measles vaccination history.