well, here’s my take on the bigger picture of taiwan’s situation/future:
they are still surviving on engineering/technology/manufacturing, but seeing margins shrink as china, india, even vietnam improve capabilities and quality. meanwhile, korea has advanced from the same eng./tech./mfg. base to building global brands. and of course japan still has the high quality perceptions. so, it looks to me like taiwan’s position/value proposition is increasingly unclear.
taiwan keeps trying to squeeze more juice from the ever-shrinking contract manufacturing and “china middle-man” roles…but china doesn’t really need a middle-man anymore.
as for more specifics, i think in much of east asia, the reality is consumer electronics. also some disposable/cute gift items, soft goods, point-of-purchase displays, exercise equipment, and of course graphics and advertising. i would say your opportunities as a relatively inexperienced westerner in taiwan are limited. salary would be low - very low as you are competing with young locals who live with parents, and this is an especially tough time to be asking a company to hire a westerner over a local. you might even try the low/no pay internship route - against my religion when you already have degrees, but up to you and your situation.
singapore market, particularly for id, is tiny. tiny.
i would think your chances in korea are best, but this would be consumer electronics with the majors - need a focused portfolio and/or big school/brand names on your cv. again, tough time to be job searching…but at least the korean majors often have rotating westerners on contract, so if some are finishing up and going home, you may find your spot. i think few other east asian nations are as open/set-up for routinely taking westerners as korea.
finally, with 2 masters (assuming they are relevant to design), teaching might be your best option. some schools are on a different economic cycle, so not suffering financially. with limited experience, you probably won’t get a real gig at a respected university, but there are hundreds of little design diploma/certificate factories all over east asia who like to hire white faces with degrees to babysit teenagers who couldn’t get into good schools.
consider that your entry point, add a little english tutoring on the side, and build from there…that’s the most optimistic picture i can paint for you right now!