hello I forget what it was but for US citizens visiting Taiwan is it no document needed if staying under 30 days? and over 30 days you need landing visa and can stay up to half year? is that it? I forget heh…thanks for the help I am heading TW on monday! 
I believe you can get a landing visa at the airport when you arrive and it is only good for 30 days. No, you can not stay in Taiwan for six months with a landing visa.
When I was there in May, they had a Visa exempt entry that was good for 30 days, and you didn’t need to bother with a landing Visa. I don’t know if that’s still true, but I’m guessing it is. If you go that rout, be advised that you can’t renew or extend it.