Mike, there were a couple different mirrors used in 1966. (besides trim options of course)
I have never nailed it down to why so I just figure it was a running revision or a regional parts issue.
Anyway, the squarish mirror on my 66 7-LITRE is not easy to find if the specific details matter.
I can find period correct looking mirrors, but not like the one on my drivers door.
Also, there was no requirement for a passenger door mirror in 1966.
If your car never had a passenger door mirror (no holes, mounts, or witness marks) then your car was ordered without a passenger door mirror and this was perfectly legal.
My Galaxie never had the passenger door mirror and I have seen a couple other 66's that don't have the passenger mirror either, but this is not common....and sometimes you have to go through the hassles of the authorities telling you the mirror was required....It was not.