Wider part up or wider part down, depending on which mirror you have. If it's a day-night item, the control goes on the bottom. If it's not day-night, it's wide-up at least through '66.
Interesting! Thank you Dan. Mine's not a day-night mirror, so I guess it's wide part up. It's strange to me how variable they seem to be. I'm seeing them both ways on cars that have likely never had the mirrors removed.