Hello from the "mainland", Ginny!
If I'm going to be any help at all, it's going to be from a distance a long way from the wonderful place you call home, but allow me to give it a try.
First of all, an answer that I can give will be based on identification info. which applies to Ford products originally assembled in any of Ford's United States-based assembly plants. That should work fine if your dad first brought his convertible into your country following its service life in the U.S.A. But if your car was originally assembled and first sold in N.Z., it's possible that the recorded "birth" info. pertaining to Dad's convertible reads differently, but I don't think this difference should prevent you from securing the licensing info. that your government is looking for.
Secondly, my tattered and a bit dated copy of the Ford V-8 annual Club Roster of members shows at least two members who are listed as international contacts for the Club's northern and southern regions of N.Z. Hopefully, contacting the following email addresses will put you in touch with one or both of them as needed:
I'll bet that if you make or offer either of these contacts a good cup of hot coffee, you'll find out all about Dad's car, how to restore it, and how to join a great old car club complete with meetings, telephone help and great people to give you a hand when it's time to turn a wrench.
Okay. I'm stepping out of the way now so you can get started. Please let us know here on the Shoebox Central website how your inquiry is coming along. I'm betting you'll have some good news to report to us pretty soon!