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This is common. Several fixes have been suggested (and tried by myself with no success) such as dimpling the ball with a punch. I gave up and replaced it so that I can address. It is simple but not cheap about $55 I recall from one of many suppliers. Remove the mirror via the allen screw, and put the new one on. Careful if you change the base, which comes with the new mirror as the screws into the door can be rusted and snap off. In my case, I had to drill the old ones out and and I used a self-tapping sheet metal screw to replace it.
I found a pretty good fix. Go to a hobby shop and get some high quality super glue. Get the medium viscousity or gap filling kind. Put a little on the ball and socket, let it set up and then break it loose. My works as good as new and has been since I did that a year ago.. Cheap quick fix,
- Put the mirror completely in a bowl with solvent for at least one hour. This will solve the glue which holds the glass in the housing.
- With a small srew-driver (or better two of them...) carefully pry out the glass off the housing.
- Then you can either re-punch the rivets that hold down the metal strap for the swivel base (will not last too long.... ) or you put a very thin piece of copper or aluminum sheet metal between the strap and swivel base (works good on my 72).
Show me a chrome mirror, I"ll show you one that flops, or will shortly if the car is driven much....
parking lots, wind, change over to later mirrors of the era....