Good info, had no idea it was this easy for work visas. When i got married here and changed to that visa they checked everything. Even gave me a squirt up the ass to make me create a sample for parasites. Quite a rude and umcomfortable experience in public.
As a thought though. Im sure you are aware. It would be very respectable to tell the staff when you go to doctors and clinics you are HIV positive. They may very well be rufe about it. But taiwan has a pretty serious lack of diligence problem
So things like bot using gloves, reusing aurgical tubing for wrapping you arm, not cleabing the table between use etc etc is extremely common unfortunately. It would be a shame if your blood accidentally spread to someone else. Not sure about the disease transfer but have seen this lack of professionalism more than 50% of the time i have gone to hospitals here
I know its a touchy subject. But just keep in mind the majority here are quite lax and if you dont want to be open about it then try and make an effort to get them to disinfect and wear gloves etc.