Here's what KF issued as the factory authorized units. The clamp on style has been reproduced and they are plentiful on eBay and other vintage parts sites. The body mount unit that matches the picture is very difficult to find so most folks go with something that looks close.
I bought out a dealer some time ago and they had, in a KF box, a mirror that turned out to be the same as 1954 Ford.
What's on your car sounds like a Yankee brand tri-bar mirror. A common accessory back in the day.