reverse wire on head unit in chevy 2500hd

I installed a Pioneer AVH-P4200DVD into my truck, a 2007 Chevy 2500HD Classic and am installing a backup camera. The head unit needs to connect into a reverse signal in order to know when the truck is in reverse. I was going to tap into the reverse output off of the BCM.

Is that ok or am I going to be putting too much load on the BCM.

Also, can I use that same positive source to power the back up camera? If not, my thought is to use that trigger to trigger a relay and then run the backup camera and the reverse input for the deck off the relay.

Powering the camera off of the reverse lamp is the safest bet.  If you know for output wire at the BCM is the actual wire that provides the 3 or so amps of current to the lamps, that will be fine.