No.740
I've never taught abroad but I did work at a university abroad. I was in the Middle East so I can't comment about Taiwan, but make sure you vet the school you work at. Private universities are notoriously shitholes that violate labor laws among other things.
If you don't want to work in Taiwan, why don't you just go to China? Again, I've never been a teacher, but I'm pretty sure all you need is a bachelors and TEFL cert to start teaching English. If you want to break from that, I assume you could study for whatever cert you need online while already abroad.