Hello. I have received my TARC. Thank you to everyone who took interest in my situation and shared advice. A sorrow shared is a sorrow halved.
I’m now the (probably only) living proof that for a TARC application, active household registration is not required. (In the sense that my mother is still alive, but is not registered anymore.) I’ll plan to write more about my case and the specific difficulties over in my thread to bring it to a closure, but I’d like to take some time to prepare because the last couple of weeks took some toil on me.
To go back to this topic’s question: To apply for a TARC, you don’t need a reason like “I want to study” or “I want to visit my family.” The “reason” you apply is a kind of criteria that you fall under, and depending on this, the required documents change a little bit.
Most typical TARC applicants can apply by being a descendent of a national with household registration who lives or lived in Taiwan, but some less popular reasons are getting employed by a Taiwanese company or having stayed for a certain amount of years in Taiwan. “Normal” foreigners can apply for an ARC with similar reasons (e.g. having stayed for a long time), but this is a different process. The TARC is only issued to NWOHRs and requires an NWOHR passport in any case.
Prepare all required documents overseas, and then simply go to the NIA in person to submit your application, or try to submit everything overseas like multipass did.
Here is the list of criteria that you can apply under, along with the required documents: https://www.immigration.gov.tw/media/42540/相關證明文件一覽表.pdf
The “code” will also get printed on your TARC, and depending on it you can apply for an Open Work Permit more easily (e.g. in the case of AF353).