First i have to reminisce a bit here ... Avital/Clifford actually offered a part for this that tied into the actual garage door inside the garage. Then the vehicle didn't even need to be present.
I have actually done this in the past though. All i did was used a relay to trigger the remote. This wasn't on a home link, just a regular garage remote, so what i did was un-soldered the button and ran it to a relay and used the alarm or an optional button inside the car to trigger the relay. You should be able to do the same thing w/ the home link. Take the visor apart, and tie into the button itself. You will want to run each side of this to a relay (terminals 30 and 87) then 85 will be your alarm trigger wire, and 86 will be your fused +12v.
If you want to find the wiring diagram, search the Toyota TIS site ... it will cost you a couple $'s but for the rest of the install, it might be help full. The stereo installer guides out there are not the best route to take for the 4runner.