I have often wondered if it’s possible to rent a car in Taiwan. Out by the airport there are some rental agencies, I think, but I can’t remember seeing any in the city of Taipei. I know that in some of the tourist resorts like Penghu, you can easily rent a car. But it’s not like finding a car rental agent. It’s just different.
In fact, one of the problems in Taiwan is making sure that your car is actually legally rentable. I would prefer to go to a more professional typical car rental chain like Hertz or Avis, but they pretty much don’t exist here.