for clarification, your parents did never register your birth to taiwanese government, right?
And, I assume you already know how to get a taiwanese passport at TECO, so you just need info on steps after that.
Notices for the Application of National Living Abroad without Registered Household in Taiwan Area for Residence in Taiwan Area
0305 Notices for the Application of National without Registered Permanent Household in Taiwan Area for Residence after Continuous residence or residence for certain period of time
If your mother is a Taiwanese and your father is a foreigner, and you were born in a certain year, there may be special rules that you may get your household registration directly.
under certain circumstances, you can.
Some of the conditions are your parents have active household registration, you renounce your US citizenship, or you get a work permit through a company.