I take no responsibility for what you do here. Don't burn your car to the ground, do something stupid, or otherwise try to blame me for what you try to modify. I'm an electrical engineer, and I know what I'm doing.
This is the resulting wiring diagram.
I chose the dome light power source in the FIAT for the power supply for the Homelink wire and ground for the system. This perhaps wasn't the best choice, but it was convenient. I found that the dome light times out if you leave the door open for too long a time. Its no big deal, since closing the door re-activates the power for the dome light. I tapped into this power supply by soldering wires onto the dome light traces. The galvanized substrate solders easily and did not deform the plastic structure of the dome light assembly.
I chose the cigar lighter as the power supply for the compass and auto-dim functions. It draws 500mA and doesn't need to operate until the key is turned on. This meant fishing a wire from the dome light area down to the cigar lighter power supply. I had already tapped into the cigar lighter for my ham radio transceiver, so tapping into it again wasn't bad. I had to gently follow the existing harnesses down the A-pillar carefully avoiding entanglement with the air bag deployment system. The wire was then run alongside the main harness on the firewall and down the center console into the cigar lighter wiring.
The resulting modification is great. I now have Homelink control over my garage door openers, the very cool auto-dimming mirror, and a compass (if I want to turn it on). The other aspect is that the standard glass mirror mount works without modification.