Ok, not a tax attorney here. So you best get the advice of one if you have substantial income.
Technically speaking Taiwan (unlike the USA which taxes your entire world wide income) does NOT tax you for income earned abroad that has no relation to your being in Taiwan.
So for example you have earnings derived from Share holdings in the USA while you physically live in Taiwan. This income is not taxable as far as the TW tax bureau is concerned. But this income is of course taxable per the IRS. You will not need to file this income with the TW tax bureau.
The money you earn in TAiwan is however possibly taxable per the IRS because the IRS taxes your entire worldwide income EXCEPT for a certain amount of SALARY/Wage/Fee payment after you meet certain criteria, such as the foreign presence test. You will still have to file this income with the IRS but are exempt up to a certain amount. But if i remember correctly you should not state that this salary income is NOT taxable per the TW govt.
So for example:
You have share holdings in the USA and got 100,000 dollars in income from those shareholdings. You must file these earnings with the IRS. Meantime you also work for an American company that stationed you as branch manager of their TW office in TAipei. And for this you receive another 100,000 US dollars a year. But you receive half of this income in the USA and half of it here in TAiwan. You must declare this 100,000 as income per the IRS but may be exempt up to the current maximum if you meet the foreign presence test, etc. But you still have to file. The TW govt will consider this entire 100,000 as income earned in Taiwan by the way, even if you “hide” 50,000 of it in the USA. This is tax evasion per TW law. But it doesnt stop a lot of people doing just that.
Now lets say that you also have investment income in a Taiwanese Mango ice shop as well as a Beef noodle restaurant and make another 100,000 USD per annum . All of this income will be subject to IRS taxation as it is not Salary/Wage income. And also be subject to TW tax office as income earned in Taiwan.
However, this brings up double taxation. A Taiwanese person making 100,000 on the mango ice and the beef noodles will only pay TW tax but not US taxes.
For this reason I do believe the USA and TW has been trying to reach a tax agreement. I am not sure what the progress is on this.
Again, im not a tax attorney by a long shot and some of the above may have changed.