Mine is from a '65 Dart. There's no clip or anything to hold the pin in, but it still wouldn't slide out. Maybe it's rusted in place; the floors are in pretty bad shape.
The pin is tapered on the passenger side, and there's a head on it on the driver's side. If it were to slide out, you'd push on the passenger side and it would slide out toward the driver's side. The studs are definitely vertical.