is the car a merc? i have that body line in my garage right now... want to say merc mirror, but not that year, or Cadillac. Someone will know this on sight, and will be along to help me eat my words.
Remove it and see if there are any factory looking numbers on the underside. There were countless aftermarket mirrors to be had in the '50s/'60s, though.
I don't know for sure, but I'd also guess it's aftermarket, from Yankee or Roberk or one of the other mirror makers, based on the fact that the mounting screw at the base is exposed. Most factory mirrors weren't like that (although a few were, so it's never a guarantee).
The mounting screws were hit or miss for being exposed, but I never saw a factory mirror that had an exposed mirror head screw...