The solution depends on how you became a NWOHR. You would need a TARC for a year then you can get household registration.
For you it sounds like getting the TARC is hard.
As you have no other nationalities you do not need a work permit in Taiwan.
There a basically 3 options
- TARC through skilled employment as mentioned above.
- TARC through family in Taiwan - this would be specific to your situation though
- Spend 5 years in Taiwan with no TARC, then you are eligible for a TARC.
Option 3 would be the last resort, it would be a troublesome 5 years. While you are eligible to work without a permit finding an employer to hire you without a TARC will be difficult. As well as daily life tasks like bank accounts and phone numbers.
As NWOHR are subject to immigration controls you would need to do a visa run every 6 months (maybe check the exact timing) for the 5 years as well
If option 3 is your only option you can get an ID number from NIA which is a piece of paper and in conjunction with your TW passport is ID equivalent to a TARC (but in reality prepare to be knocked back)
Also TECO are lying to you. It is TECOs responsibility to accept TARC applications for NWOHR in other countries - I applied for mine at TECO and I had to complain before they accepted the application. They will give you a printed version of the TARC which you exchange for the card in Taiwan