I have a US passport with a visitor visa valid for 5 years. It is a multiple entry visa for 60 days at a time. I was in Taiwan for 4 months, so I went to Korea for a weekend (not to a visa office, just for a visit) and came back to Taiwan with no problems. They just stamped my re-entry date and sent me on my merry way. Before my second 60-day stint was up, I came back to Michigan to sort some things out. I live in Detroit and am a professional musician.
My question is: If I go back to Taiwan, can I just keep going on little visa hops every two months until 2005? Am I still limited to six months in any given year?
What you have is a short-term visitor visa, which is often also called a tourist visa. As you have stated, the type you have is valid for five years, and each stay may be sixty days. If this visa (in your passport) is not marked with any particular restrictions, it would also be possible for you to extend it in Taiwan for an additional sixty days, and then another sixty days, before leaving the country after six months.
Your problem is to find an acceptable reason to extend the visa in Taiwan. One common strategy is to sign up for full time Chinese language lessons at some local language school which is government approved. It also might be possible to find a calligraphy school, martial arts school, Chinese medicine school, or other schools that are government approved, and that have classes for foreigners.
After living in Taiwan for six months, you can go to H.K., Korea, or wherever and come back the same day or the next day. Then you can begin another period of stay in the ROC. There is no specific rule that denies you the right to be inside the ROC over six months per year on a short term visa. However, you have to renew at the end of each sixty days, and then you have to leave at the end of each six month period.