All I did to get it working (wiring-wise) was to just add some wiring from the passenger side mirror (which seems to always be on) over to the driver's side, paying attention to neg and positive.
At that point, I could see the little red LED lighting up when I pressed the buttons.
Then we went through the programming instructions, first with the remote and the visor, and then pressing the button on the opener itself, and voila, like magic, it started working.
Only thing of note past that is that I've noticed there is a slight delay when pressing the visor button to open the garage door. Seems like the 'real' remote you just click it, but you have to hold the button on the visor down a little longer. A slight click and hold, until you see the garage door move. If you just press it quickly, it's not going to do anything.
Is the light on the mirror working on the Homelink visor? Since there's only one pair of 12V+/ground wires going to the visor, they obviously share the same power source.
Also, I'm not sure if the Homelink hardware in the visor would lose its programming if you have it on switched 12V power, so it powers completely down when the car is turned off. Mine is wired to unswitched 12V+ - the visor mirror lights work all the time.