One of the mirrors on my scooter sags while I am riding, so I have to keep
pushing it back up. It's the usual sheet metal ball-and-socket joint, and
does not appear to have any way to adjust the tightness. Does anyone have
a suggestion that might help? Lok-tite, maybe?

My standard trick to increase friction is to peen it with a center punch.
You want to get a couple peened areas under the socket.

Karl