Just to echo what has already been said.
We just picked up our TRNs today. It was quite painless. We used the information on this government web page:
http://www.capetown.gov.za/City-Conn...ister%20number
We are two Canadians, just arrived in Cape Town a couple of weeks ago. Last week, we went to the Motor Vehicle Registration and Licensing (Civic Center on Hertzog Blvd) and handed in:
- Filled out Traffic Register Number Application Form (download PDF from the link above)
- Passports
- Two passport-sized photos
- Proof of residence
The lady at the counter did not seem satisfied with our papers. Officially, they want to see a proper 6-month or longer visa (work or education preferred) in your passport. Instead, we had a 90-day tourist visa exemption stamp. Strike one.
Also, we handed in a printed-out copy of our AirBnB reservation. It was only for two weeks...

She shook her head and said that "hotel reservations" did not count. Strike two.
However, she took all our papers and told us she would forward them to central processing and they would determine whether we would get our TRNs approved or not. She warned us that it was doubtful that it would happen, but to come back in 7 days and check. So we left a bit dejected.
Went in this morning, and to our surprise, the TRNs were approved!