I don't recommend staying in Taiwan.
Local companies aren't a lot of fun to work for. The very best case scenario for you staying in Taiwan is to find work with a Western company and climb the corporate ladder in say a representative or branch office. Unfortunately, you're not offering much to such a company. Right now, you're not offering them fluency in Mandarin, long-term experience in Asia, or a working background in your field either in Taiwan or overseas.
In other words, you're competing against locals at the entry-level, some of whom will speak English much better than you speak Mandarin, and almost all of whom will be satisfied with a lower wage than you'd earn teaching English.
Teaching English is a trap, especially with your education. I strongly recommend you save yourself years of heartache and establish your career as soon as possible in a Western country. You'll soon find yourself earning much more than if you'd stayed in Taiwan, and you'll start building whatever pension you might be entitled to when you hit retirement age. Maybe you'll also buy a house, which won't even remotely look like a good idea in Taiwan until you realize house prices have gone up 1000% while you dithered and you could have made more money buying a house and NOT working the last ten years.
Western companies of any type will NOT value teaching experience in Taiwan, and unless your Mandarin is at a very high level and they need you to do business with China they won't be impressed with your Mandarin either.