According to the Taiwan Central Epidemic Command Center, if you are 18 or older and holds a valid NHI card, you may now pre-register for COVID-19 vaccination (until 12:00 pm on July 19). After the pre-registration deadline, eligible people will be notified by text message from July 20 onwards and only those who receive the text message can make an appointment for vaccination.

Source: https://www.cdc.gov.tw/En/Bulletin/Detail/Gn-TIERW6HQL0awMxHuTkg?typeid=158
For instructions on how to use the COVID-19
Pre-registration Platform, please visit https://oia.ntu.edu.tw/en/board/detail/sn/1278