I assume you are "living" there on a tourist visa. Reading http://www.ntat.gov.tw/county/ntat_ch/n ... en9-04.jsp, I think they intend to tax foreigners living there, even if they don't work there or have permanent residency.
5. Q: What is the definition of a resident of the ROC?
A: Someone whose circumstances fall under any of the following conditions shall be a resident of the ROC:
(1) A person who has domicile within the territory of the ROC and resides within the territory of the ROC; or
(2) A person who has no domicile within the territory of the ROC but resides within the territory of the ROC for a period of more than or equal to 183 days during a taxable year.
You seem to meet criteria (2). It doesn't say the 183 has to be continuous.
Taiwan's AMT seems to kick in when you make 6 million NT dollars (About USD $191,000) and 1 million NT dollars (about USD $31,800) come from overseas income though might not necessarily pay more.
As for tax percentage, this will let you calculate it.
http://www.ntat.gov.tw/county/ntat_ch/n ... 04-2-8.jsp
8. Q: Is an individual who has a basic income greater than 6 million NT dollars necessarily required to pay basic tax?
A: No. An individual who has a basic income greater than 6 million NT dollars is not necessarily required to pay the income basic tax. There are several steps further to go.
(1) Step 1: To figure out the amount of Income Basic Tax.
The Amount of Income Basic Tax ＝(The Amount of Basic Income - 6 million NT dollars) × 20%
(2) Step 2: To compare with the amount of income basic tax and the amount of regular income tax.
The amount of regular income tax* ≧ The amount of income basic tax
An individual shall pay the income tax in accordance with the Income Tax Act and does not have to pay the income basic tax.
The amount of regular income tax* ＜ The amount of income basic tax
The difference between income basic tax and regular income tax can be credited because of income tax paid on the overseas income. So the amount of income basic tax payable shall be the sum of aforesaid difference minus the income tax paid on the overseas income.
* The amount of regular income tax ＝ Income Tax payable in accordance with the Income Tax Act - Investment tax credits
But this brings up the question, how will Taiwan know what you make overseas? Can they gain access to those records? Are they going to start requiring that you fill out a tax return once you hit 183 days and they notice you haven't done this when you try to leave the country?