Which glue
Here is a post on fixing/replacing mirrors. He used JB Weld.
I had complete success by applying a dab of clear silicone caulk/adhesive to the top of each corner boss in the chrome fixture, then pressing the mirror glass on and clamping (careful not to apply clamp directly to the glass) while the silicone cures.
I replaced glass once, removing repro glass from a repro mirror and gluing in a dated original with absolutely no complications. I removed the old glass by soaking the entire mirror head in lacquer thinner over night. The old glass lifted right out with no problems and no damage to chrome or glass.
Hope this helps.
Use Permatex black RTV for that job. It will stay flexible and it will last. Also, when you glue it, you need to 'stage' the glass on something very flat...upside down...then place the mirror body upside-down on the glass. That way the glass is not distorted by the weight of the mirror body. It also won't be distorted by its own weight, if you were to try putting it together right-side up.
Styrofoam blocks on the glass/mirror face and a couple of wraps with masking tape around the fixture got the job done.















