If I remember it right, it’s actually called a visa exemption. Don’t confuse it with a 4 week landing visa which you have to get at the visa office at CKS before you go through immigration and which will cost you 2000 NT and a couple of passport pictures. God knows, I was completely confused with visa exemptions, landing visas, visitors visas etc.
For the visa exemption, ignore the visa office at CKS and just walk straight to immigration. They may or may not ask how long you intend to stay, they never asked me when I travelled here for months in a row. The only form you’ll have to fill in is the usual landing form they’ll give out in the airplane.