For that I would try little tiny balls of blue tack.  Barely tap/stick the mirror to the blue tack so it will easily pop off.  That way it won't' slide around on you.  A drop of CA in the hole, let it sit for a few seconds.  Use your tweezers to gently place the bracket in place.  Then don't touch! for a few minutes.  Use the tip of the tweezers to adjust the positioning if needed, not you fingers.

I'm also looking to invest in a "jewlers" headset with the adjustable magnification.  Anyone know of affordable brands, etc.?