Part-Time Work Online

If you teach online on a part-time basis, and you are on an ARC in Taiwan
with a work permit for a specific school, would it still be a breach of the
contract if you do a part time job teaching online during your down time
as long as the employer is not based in Taiwan?

to be gray, iiuc,
customers and employer should not be Taiwanese too, regardless where they are based.

Nobody is going to care unless if interferes with your ARC job. That’s how things work. Taiwan, while inconsistent in enforcement of many laws, only seems to nail people when someone gets hurt or loses face. My employer tells me I am forbidden to do ANYTHING passive or active outside of my work. If you aren’t doing something else then I say it’s a bit unwise. You open yourself up to being bullied and manipulated by your employer because you’ve nothing going on the back burner which will give you confidence to stand up for yourself. If your boss is generally okay with your performance, and you aren’t becoming the face of the other company with online profiles, etc…no one will likely know or care.