Hey Steve,
I did the same thing after I got my APRC. Just go to the NHI office by taipei main station (I think it’s the fifth floor), tell them you don’t have a job and then wait around for about half an hour while everyone talks to each other to figure out what to do with you 
After that, they’ll tell you to go home and wait for your bills, which you can pay at the 7-11 just like anything else. I was charged $749 a month, although the first month was twice that because I didn’t change things over as soon as I left my job. It’s actually a pretty easy and painless process.