Now you're getting into a few of my learned little tricks of the trade on my '82. What you're trying to do was necessitated on mine because it seems nobody sells silver gray interior parts that match properly and my vanity mirror was deteriorating (silver coating was delaminating from behind the glass) . And, my wife appreciates having a mirror there. So, I carefully popped out the old mirror from the hard plastic surround which is affixed in it's soft vinyl insert. I used a screw driver but in hindsight I probably should have used a wide putty knife to reduce strain on the mirror, and maybe sprayed a little silicone lube into the back while pried back a bit and let it sit overnight. But all worked out well when it popped out from it's two unseen affixing tabs located squarely in the middle of the mirror, on the back. Now, with the mirror and it's soft plastic surround in hand I carefully peeled it out of its insert. It came out easy on a warm day because it's surround is soft vinyl/plastic. I then purchased a wall mirror at Target (well under $10) and traced out 3-4 mirrors with the old one as a template, using a Sharpie marker. Then, I cut them out using a new glass-cutter by putting a thin film of oil on the new mirror as directed in the glass cutter instructions. Just do it confidently, push down and cut and don't be wimpy about it. Cut with purpose. The new mirror size needs to be identical so measure twice and cut once. The new mirror from Target was a little thinner and more bendable than the old one but you cannot visually tell this when it is installed. It looks like a brand new factory mirror for that matter. I then just very lightly siliconed (clear color) the new mirror into the plastic insert that I had peeled the old one out of. Once it was mostly dried I popped it back into the vanity mirror seat held in by the two vinyl tabs that are in the back, middle of the mirror. I broke two mirrors while re-inserting them (and one while cutting them), until I silicone-lubed the the two small affixing tabs, then it slid into both holes. Most important of the whole upgrade, remember to ONLY push on the new mirror precisely on the front of the mirror where the two insertions tabs go into the holes behind the mirror. This will minimize flexing and breakage since the new mirror is thinner than the original (again, this is unnoticeable). If it takes a few tries and you go through a couple of mirrors, you're still WAY ahead cost-wise, even if they happen to offer your interior color. Bottom line, my wife was very pleased with having a usable, brand new mirror.
Btw, I also added a micro rocker switch to operate the vanity light because the cover that turns on the vanity light switch was missing when I bought my otherwise mint car (and, again, none of the C3 suppliers sell a silver gray vanity mirror assembly). I'll tell you how to do it using a hot knife (or, craft knife and a propane torch to heat it) to make the small, rectangular hole for the micro rocker-switch that looks like an OE installation, but probably that's for another posting someday.
Good luck. Dave
Lakeside 49