Emulating the Havana School of Auto Repair

In Cuba, 1954 Chrevolets, Fords, etc, are still running. Although they can't import parts, they go with sturdy, but home-built fixes. In this article, we address the rusted off mirror.

So you went to adjust the mirror and it broke off in your hand?
First, here's how they come off. Lift and rotate the plastic cover to expose two phillips screws. jj Then carefully pry off the plastic bezel and the mirror lifts out. The bezel may crack on removal. Oh well.
Plan - Remove the broken rusted bolt in the mount.   All of this hardware is found at a (what else) hardware store.
If you need the ball, scrounge around for whatever works!   Mechanical parts in. Just add mirror and glue on the bezel.