"Mike Rocket J. Squirrel Elliott" wrote:
....
I have only access to the side /inside/ the medicine cabinet. The other
side is buried behind the plaster wall.

....

All I can say is "plan ahead"...

Drill pilot and go slow...after drilling if needed you can epoxy over
any loose area on the inside and let cure. If similar to Soss,
depending on the size, you may just epoxy it in place.