Spray some salty water on is and let it sit outside under some pine trees for a couple days. It'll seize right up.:grin:
I believe on a convertible there are screws you can tighten as well on the inside mirror. The glass does not need to come out.
I have this exact issue on my 61. Door exterior mirror moves. It's so loose a slight breeze will move it. I'm forever readjusting it. I tried super glue and it lasted 3 weeks before it just cracked and fell out and loose mirror again. This weekend I'm trying a clear silicon like used by tilers. It flexes, so won't crack like hardened glue, clear so won't be seen, but has some setting / glueing properties. Will let you all know how it goes.