You are real Overseas Chinese (華僑) qualified to waive military obligation.
IF you wish to stay over one year, you can get a "僑居加簽 Certificate" at the 僑委會. Bring that "僑居加簽 Certificate" to Taiwan INS for a "僑居加簽 Visa" on your Taiwan Passport. Then, you're free from military service like me.
For short visit, you can use both passports in "any combination" you like to visit Taiwan. (Your civil right of education, medicare, etc., can still be declared at any time you show up Taiwan Passport.)
* I'm 19 yo ABC in Taiwan for years. I claimed my "僑居加簽 Visa" for my Taiwan Passport this year. No military hold on my Taiwan Passport ever.