iiuc, you can work at other places without additional work permits, but to keep your work ARC, you need at least a work permit through one of your employers. There is another interpretation that as far as you are on work ARC, you need a work permit for every job.
labor insurance and (un)employment insurance are different.
Employment insurance is only if married to an ROC citizen.
To protect workers’rights and avoid penalty, business entities should enroll in Employment Insurance as long as they have employees
https://www.bli.gov.tw/en/0014523.html