We used to repair the 68-76 Corvette mirrors like this.....
Remove the mirror from the door and soak the whole thing in lacquer thinner overnight. The thinner will soften the adhesive to the point that the glass will be easily removed, but will not damage the silver on the back of the glass. You can then make any necessary repairs behind the glass. To reassemble the glass to the mirror use a suitable 2 part adhesive.
If you don't feel confident to do the repair this way, you can "cheat" and use a center punch and a hammer to "dimple" the rotating ball like this....
Rotate the mirror head all the way up as far as it will go. Then use the center punch and hammer to make a dimple in the round ball. This will raise the material around the punch mark, effectively tightening up the mirror head once the mirror head is rotated back to its original position. This method doesn't always work, and usually will only last for a short time if the mirror head is adjusted repeatedly.
Good Luck!!
George