A flush mount angled camera would be your best bet...single hole, one and done. Drilling into the liftgate (or truck, for that matter) takes a little courage, but mask it off, double check your clearances inside the liftgate (particular for the wiper motor and linkages), and take your time.
It is possible to get wiring through the liftage tube/grommet going into the chassis. I've run wiring there previously for some LED lights I installed. Just need a rigid wire to fish/pull wires through, and removal of all the trim liftgate trim and weatherstripping.
For the reverse signal, you've some options:
Behind the front passenger kick panel, one of the harnesses has a yellow wire that is the reverse signal. The harness will depend on whether it's AT or MT, but they're in the same area. The FSM details it (I can help with more info about your truck).
Many cameras will have a power wire "tail" at the RCA side and a positive and negative lead on the camera side. The camera-side wires can be tapped into the reverse signals at the tail light with the pos/neg wires (or just pos from the reverse pos signal and ground the neg wire). You can then connect the tail wire to the reverse signal on the radio, without having to use the reverse signal from the kick panel. (The tail light will power the camera and signal the radio.)
If the camera side signal wires aren't long enough to reach the tail light (plausible in your case if installing on the lift gate), but you plan to use the reverse signal at the kick panel, you can cap the pos wire at the camera side and just ground the neg wire. You then need to connect the reverse signal, radio reverse wire, and the camera's tail wire together (this will send the radio the signal and power the camera).
If the camera lacks the tail wire, you'll have to use the reverse signal from the kick panel for the radio signal, and also the tail light for the camera's power leads.
Note that if your radio supports live camera viewing, you won't be able to utilize this camera for it because the camera will only be powered when in reverse.
I recently added a reverse camera to my truck as a Phase 1 project, and while it fits the immediate need, it's not the end product. Because of the tire carrier, I made a bracket and ran the wires externally along the frame:
This setup is temporary, and I may even redo the camera mount to center it in the hub. Phase 2 setup will require rewiring this camera completely as part of a quad-view setup using front, rear, and forward- and rear-facing undercarriage cameras for trail use. The live views of those will probably make my wife throw up.