Hello, My name is Mike, and I can help with this question. First I need to know one thing.
Is the mirror loose where it contacts the glass? Please describe what part that you see being loose.
Thank you,
Mike
Ok, Thank you for this information.
The dealer is correct when they quoted you for a new mirror. This item is technically non serviceable. You do have some options though.
If you are comfortable with removing the mirror from the glass, do so. That way you can get to what you are looking at without contorting yourself.
Now you can identify if this is something that you think you can get to come apart, and if you want to try. You could also wiggle some pieces of thin felttape into the ball and socket. peel the backing out of there after it is in place.
If all else fails, re-install it on the window and position it with tape or even epoxy it, although these wouldn't be the ideal solution for your Corvette.
Contact salvage yards in your area to see if they have a mirror before you buy a new one.
I hope this provides you with your options.
ASE Certified Technician
20 years experience, all makes and models.