I just thought I'd update this post, since I popped the mirror out over the weekend. I put some mineral spirits into a small squeeze bottle and dripped it all around the edges multiple times. I also put some in from the back by dripping it around the pivot ball. Truthfully, I am not sure any of that was really necessary with the older style (small metal frame, curved glass) mirror. But I heard once that the later (i.e., SV) mirrors were attached with double stick tape, so that would certainly be the way to go with those.
The mineral spirits certainly didn't hurt, but the key for me was trying to figure out what to use to gently pry the mirror out. It looked like a razor blade would be perfect, but that seemed very likely to chip the mirror. Then I remembered the tool that had come with the replacement battery for my iPod (
http://www.ipodjuice.com/AB4F1D8928...30B707A4ABB.asp&nm=bmTOOLINSTR3G&spath=&path=). It was perfect. I was able to gently edge it into the frame along the lower edge and very gently pry upwards. I had the best ‘grip’ there, but also worked around a bit on all four sides. Then, back to the lower edge and the mirror just popped out! I can now see that it was glued along the edge to the frame. The glue that is left on the frame seems pretty hard, so I don’t know if the mineral spirits had any effect or not.
The mirror is now off to be resilvered. The next tricky step is deciding if I should remove the arm from the housing or not. The chrome on the arm is in surprisingly good shape. A few pits here and there, but not bad and certainly better than the one I am using now. However, the housing is pretty rusty and I could do a much better job cleaning it up and repainting it without the arm there. However, removing it would require drilling out the two rivets and it has been a long time since I've done any riveting other than Pop Rivets. I am not even sure how readily available such rivets are. Does anyone know?