Today, I tore apart the driver's side mirror to see what was the cause of failure. (Attached picture of instructions on taking the painted mirror cover pieces off.)
About the motor housing with the broken pin, plans are to:
Use a dremel to shear off the unbroken pin.
Purchase two ~6mm long / ~2.5mm diameter steel dowel pins (need to grab calipers from work and take exact measurements)
Drill two holes through the motor housing where the sheared off pins used to be.
Drop steel dowel pins into motor housing pedestal
Align motor housing with new holes into the pedestal/steel pins
Should be a stronger permanent fix.