please see the inside box.

there are a few car rental companies in Taiwan.  I used Gharry. Online rental and put all your info (including passport number,  Airline number, arriving time,  pick up time........).   You need a AAA issued international driving permit for driving in Taiwan.  Fee ranged about $80-150 /day,  depending  what type of car you rent. 

https://gharry.com.tw/en/index.php?clang=us