I don't know about removing the mirror button but I have reinstalled them a few times.
The glue specifically designed for this seems to work OK -sometimes. I don't know how it decides to work well or not. It doesn't seem to have anything to do with the installation though.
The best thing I have found is silicone sealer/gasket maker. Just make sure you clean the window with rubbing alcohol first. You can get blue, red, black, clear, maybe others. I put a mirror back on an old Rabbit with this stuff. When the car was finally on its way to the junkyard I removed the windshield. Some time later I needed the mirror button for another ride and ended up breaking the windshield trying to remove it.
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Jim
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