You'd need to find out the wire that tells the NAV that you are in reverse. Usually, this is the reverse lights. To do it correctly, you'd need to power the wire but not the backup lights. This would mean when you push the button it flips 2 relays: one to power the wire, and a second that cuts power to the lights.
There is a reverse wire that comes out of the Nav box under the passenger seat. I have my AVE navswitcher box hooked to that so that when there is a signal it flips up the camera video source. Mine is aftermarket though. I don't know if I would mess with it without first knowing what it might f'up. I know the reason the wire is there is so it keeps track of you in the gps. With everything interconnected by the CAN you might screw something up if when going 70mph and all of a sudden something gets the signal that you are in reverse.
I can flip the camera on though without being in reverse when I want. It's kind of cool as it feels like a video game but I can only handle watching for a few seconds before I start to feel like I'm going to get sick.