I’m assuming you are not married to an ROC national, or else you wouldn’t have a visa problem (right?)
An Article 51© work permit is what I’m talking about. This is teh category for “garden-variety” normal foreigners, who are not a) married to Taiwanese, b) stateless refugees, etc. etc. (all the OTHERS get unlimited open work rights, but we do not.)
You need to prove 5 years worth of ARC-carrying legal work, plus documents from the Bureau of Entry and Exit (NT$100, no sweat there) showing that you made 183 days each of those years. You’ll need a contract hiring you, with the chop of the company and the responsble person, and (later) a written statement that you are indeed working for the company (to get your ARC after you’ve got the work permit). The application form is 1 page, one sided, and is very, very simple; little more than name, rank and serial number.
This section © Article 51, however, only allows you to work for one specific employer. It is better and easier than an ordinary work permit because as a foreigner, for a 51 the employer does not have to prove that he needs a foreigner to do the job, does not have to have a minimum capital in the business, and doesn’t “sacrifice” a slot for a foreigner’s (normal) work permit for you. You don’t count toward that company’s quota of foreigners.
You can get the forms at the CLA on Yanping N. Road. They’re fabulously helpful (really.) Best thing that ever happened in Taiwan IMHO (only, I do not see why WE should not have open work rights instead of “just partly open”, but hey, something’s better than nothing, I guess.)