I asked the guy in charge on Caye Caulker, he said residency is required, it wasn't for me in San Pedro?
It is very common in Belize to get several different answers to the same question.
google this link in Belize city, it says all you need is SS card for first permit, nothing about residency.

Procedures of Traffic Department - Belize City Council - Government ..

It also states that you cannot get a class C (taxi permit) unless you are a Belizean.
I got a class C last year before applying for citizenship, no problem at all.
Catch the right guy on the right day and you can be Prime Minister.