I just installed a back up camera on my Volt last week. Just wanted to share my experience since my Google search for help turned up this thread. I'm sure more people will be looking for this information, and I wasn't able to find any good sources in my quick searches.
To answer the original poster's question: My experience, after trying several methods, was to just tap into the back up light wiring under the rear bumper. Better said, right before the plug for the back up lamp. I tapped into the wires just before the plug, and soldered my taps on, then covered with heat shrink tubing. I ran the tap wires (power for the camera and monitor) up behind the bumper.
The bumper does NOT need to be removed to do this (tapping into the back up lamp), however the lower "aero" tray should be removed or at least moved out of the way. The tap wires can be run through an existing plastic grommet that is accessed inside the hatch, once the rearmost panel is removed. I also ran the camera's video feed cable through that hole/grommet.
My particular camera had a single cable to the front of the car, which I routed under the driver's side sill panels, which are pretty easy to remove. Then routed behind the dash and up through the fuse panel door between the dash and car door. No drilling of the dash was needed. This particular camera suction cups onto the windshield.
I did try tapping into the fuse panel in the hatch, but those fuses seem to be always powered, so the camera was on regardless of the ignition state. I also did try to remove the bumper to make this whole process easier, but chickened out after removing all clips except the ones right under the taillights, which seemed to require more force or knowledge than I felt like applying.
I should note that the camera does turn on when locking the vehicle, since the back up light is illuminated (along with the headlights) for 30 seconds when the car is locked. This can be changed in the car's settings.