96 LSS
OK, I give up before I completely destroy the plastic housing rear view mirror base around the metal "button" that glues to the windshield!
My rear view mirror was simply hanging from the electric cord after the glue that held the metal button to the windshield for +-26 years has finally let loose.
Attempting to remove this button so it and only it is dealt with re-attaching it to the windshield.
The button seems held in place in the base of the mirror by the standard metal clip, which has about a +-ton of grip power, which is what ya want when fasten to the windshield, but not for simply removing the button from the mirror base.
There is no simple little screw (like some vehicles have) that one can loosen, relieving pressure holding the button in the clip.
Once the button is glued to the windshield, there is a stop piece of plastic preventing the mirror base from sliding too far, but this plastic is in the way of using a larger prying lever to lever the button free of the base/clip. The only areas to slip any lever in is on each side of this plastic stop block, but the openings only allow for something in the neighborhood of +-3/32nds inch diameter, which doesn't allow for many levers which have enough tensile strength to do this job.
Help! Any suggestions? What's it take to get this dang metal button removed from the mirror base clip so I can epoxy the button back to the windshield?

 

Well, never mind, no need to reply, I got it! Phew! Caution: The button did go flying when it popped off, so be prepared for that, if ya have opportunity to mess with re-attaching your mirror, with a button that snaps in place and hasn't a tension screw.
Found that I could remove the bulk of the mirror base plastic cover by prying out on the two keepers on each side by the button sides, which held this base plastic in place, then carefully removed this piece from the mirror stem through the slot in that plastic base. Once that piece was removed, that allowed more access with levers to beneath the sides of the button to pry it off.
I drove two separate philips screwdrivers (with +-3/32" shank) into each 3/32" hole on each side bottom edge of the button. That seemed to give a little space under the button allowing a regular mini screwdriver to be tapped in beneath the button. Prying down on the phillips screwdrivers while prying up on the standard screwdriver, and "pop", the button was sent flying across the room.

And the button is now glued back on the inside of my windshield, with mirror base attachment sliding on the tapered button pending it thoroughly drying to the windshield first.

Thanks for all the help, that is, kinda sorta forcing coming up with my own solution through further investigation.