I have done it MANY times on vehicles. Very easy job.
I use just normal Black RTV and coat the back pretty well and around the edge in hopes to seal out water as I felt if water would get in that it may freeze, expand and break the glass. Install the glass by simply pushing it in place, so not too much RTV, just enough to do the job. You will want to get a towel and ball it up so that it is taller than the mirror frame. Set the balled up towel on the glass, wrap another towel all the way around the mirror and the balled up towel. Then wrap black tape or duct tape around the towels. This will keep pressure on the glass. It is easy to remove as nothing it actually stuck to the mirror. I have always left it on for 24 hours.
I never broke one and I have never had one fall out as the customers have never come back to complain,,, (I'm sure they would have if it fell out).