Can a Taiwan National without Household Registration (NWOHR holding a TARC) work in Taiwan?

I am a US/Taiwan dual citizen who recently moved to Taiwan and just got my TARC through blood lineage. Do I need anything else to be able to work in Taiwan? Do I still need to apply for a work permit?

If so, does my employer apply for me? Or do I apply myself? What government agency do I apply from? Is it an open work permit allowing me to work pretty much for any company (except government, etc.)? Or is it tied to a specific job (ie will I need a job offer)?

Followup question: If I choose not to work, can I still qualify for National Health Insurance? I really don’t want to wait a full year until I can get an ID card.

I think you need a work permit as far as I know, but @tando knows this more than I do.