If your grandparents never lived in Taiwan, then I think you are right, they probably never got an active HHR. Unfortunately, I think AF384 only applies to children of a national who has or had an active HHR in the past. If your grandparents (parents of your mother) did not ever have an active HHR, then your mother is the child of an NWOHR, not a child of a national with HHR. And as far as I can remember, I don’t think I saw any discussion here about any cases where a child of an NWOHR can apply for a TARC under AF384.
Under the logic of AF384, I think the required sequence of applications would be:
- Great-grandparents had HHR in the past.
- Grandparents, because they are children of #1 who had HHR, can apply under AF384 for TARC and get their own HHR.
- After grandparents succeed to get HHR, then their child (your mother) is now a child of (a direct blood relative of) a national with HHR. Their child (your mother) now belongs to the category of “有直系血親在臺灣地區設有戶籍者” (Those who have direct blood relatives with household registration in Taiwan) and can apply under AF353 for TARC and get her own HHR. Maybe AF384 also would also work here, because your mother is also now the child of a national with HHR – but maybe AF384 might not work if the NIA says the HHR of your mother’s parents must have existed before your mother’s birth; see Reddit - Dive into anything for related discussion, which says " This is the same situation that prevents me from getting my heritage citizenship, as my mother could apply now, but since she didn’t do it before I was born, I am ineligible no matter what as their jus sanguinis is restricted to a certain number of generations at the time of birth."
- After your mother succeeds to get HHR, then her child (you) is now again a child of a national with HHR. Her child (you) can apply under AF353 for TARC and get your own HHR.
What you are trying to do is skip step #2, and use #1 to support #3. In other words, your mother is the grandchild (not the direct child) of a national with HHR.
Unfortunately, I have not seen discussion here on the forum about this case. Furthermore, another discussion on reddit also implies it is not possible. See Reddit - Dive into anything which says:
question: would a NWOHR under age 20, with grandparents who have household registration (parents do not, are only NWOHR) be eligible to automatically register for household registration the same way children of NWHR do?
…
answer: None of the relevant laws mention grandparents, so my guess is no.
In order for you to succeed with AF384, I think that you would need to prove that the requirements for AF384 (https://www.immigration.gov.tw/media/42540/相關證明文件一覽表.pdf), which says “居住臺灣地區設有戶籍國民在國外出生之子女，年齡在二十歲以上”, includes not only the direct child of a national with HHR, but also includes the grandchildren of a national with HHR. I really don’t know if that argument is valid or not – my Chinese sucks, but the presence of the word “出生” seems to mean AF384, interpreted literally, applies to children who are born directly to the national with HHR. In order to argue that this AF384 condition logically should include grandchildren as well, then I guess you would need to hire a specialist lawyer who could make that argument based on the spirit of the law and based on past case history (if there are any successful similar cases in the past).
A lawyer could also advise you about any other options you might have.
I’m sure that there are people here on the forum who know more about this than me. Would anyone else like to comment?