Interestingly, TAS have removed the foreign visa/ARC requirement for admission in the past few years. They were the last holdout of this old rule.
This post quoted the TAS website in 2019:
Q. Must a student hold a valid foreign passport and visa to enter the school?
A. Yes. This is required by both the ROC government and TAS admission policy. No exceptions are made.
Compare with the latest TAS website - mention of “visa” is removed:
https://www.tas.edu.tw/admissions/application
Q. Must a student hold a valid foreign passport to enter the School?
A. Yes. This is required by both the ROC government and TAS admission policy. No exceptions are made.