Answer:

1. Since January 2, 2007: 

(1) The Taiwan Alien Resident Certificate has been issued by the National Immigration Agency and bears the “Taxpayer ID No.” for Hong Kong and Macau citizens, PRC nationals, and overseas Chinese.

(2) ARCs are issued by the National Immigration Agency. They bear the “Taxpayer ID No.” for foreign taxpayers who reside in Taiwan.

(3) Foreigners or nationals without registered residence in Taiwan can apply for the “Taxpayer ID No.” in person or by proxy to the National Immigration Agency by submitting their passports; Hong Kong and Macau citizens, PRC nationals, and overseas Chinese can apply for the “Record of ID No. in the Republic of China” to the National Immigration Agency.

2. The “Taxpayer ID No.” was originally composed of two letters and eight Arabic numerals. 

The National Immigration Agency, Ministry of the Interior released new ID Nos. on Jan. 2, 2021. The replacement period is from January 2, 2021, to December 31, 2030, and the original ID No. will be invalidated completely from January 1, 2031.
The new ID No. is composed of one letter and nine numerals. 

For instance:

(1) Mr. Robert W. Davison’s old ID No.  is “AC12345678.”  His new ID No. would be “A812345678.”

(2) Ms. Carol Lee’s old ID No. is “HD12345678.”  Her new ID No. would be “H912345678.”