From what I can tell in general and from my application, as long as your ROC parent has had a household registration in the past, the tracks are set up to you being able to receive a TARC. However, the “quests” that you need to complete and the documents that you need to collect will largely decide how difficult the process is, and whether you need your father’s involvement.
Your case is special in the fact that you were born before your parents got married, and the NIA has a special note for this:
Unfortunately, I cannot tell you how easy this is to achieve since we haven’t had this case before (as far as I know). The rest would depend on whether you are able to convince your father to return to Taiwan to re-activate his household registration. As long as the above note does not require your father to do anything in Taiwan, then you will be able to apply for a TARC without your father’s presence.
From my point of view, you have a chance; but keep in mind that there are basically two deciding factors: Whether you fulfill the TARC requirements by law, and how easily you conform to the NIA’s SOP.
Something to keep in mind if you cannot, for whatever reason, get the required documents for children born out of wedlock—consider my case: I had every document that the NIA asks for, but they wrongfully assumed that the Immigration Law would not apply to me, and this is why I had so many difficulties. But the law was on my side, and thus I was able to proceed. In your case, the law pretty clearly applies to you, and you may or may not be able to argue with the NIA about that. What I mean is that the law itself doesn’t say anything about all of these required documents—it is all the NIA’s implementation.
But this is just to show you another perspective if you inevitably experience your first setback. In any case, I would advise you to first apply for the NWOHR passport. You will more or less only need a translated copy of your birth certificate.
(If you were not born overseas, then you should tell us, because this would make all of this a little bit different.)
Some concrete details for your case:
my father was born in Taiwan and moved to another country many years later
So he has a HHR registration; this means you are a National, and you can apply for a TARC.
he met my foreigner mother and I was born. They got married one year after my birth.
This is the special thing about your case—you being born before your parents got married.
His HHR was no longer active by then.
Irrelevant for your TARC application.
I’m over 30.
A pity, if you are younger than 20, you’d have it a lot easier.
TECO believes I have enough documents to get a Taiwanese passport
I don’t have direct relatives in Taiwan.
Your aunt doesn’t play any role in your TARC application. It will revolve around your father’s old HHR, and whether he wants to re-activate it or not.