If you can post a pic of your mirror always helps.
Fill the holes with plastic tooth pics ( plastic wont absorb moisture )
packed tight and epoxy is another option.
To be a little clearer to be safe I taped off around the hole in need of repair. Wore rubber gloves and dipped each tooth pick in epoxy inserting them into the hole untill packed tight with tooth picks.
Let dry and drill small pilot holes...and re-mount your mirror.