black can go straight to earth/ground and red should go to the power side of the reverse light /bulb socket so that it only powers up when reverse is selected.
How much does the camera draw? Tapping the power into the reverse light could cause some blown fuses, if you do go that route make sure you use a relay so the draw is minimal.
Also how long does the camera take to power on before it shows the video? Might not be the best route if there is a delay.
just use the signal from the rear lights to trigger a relay that turns on the camera. Run a dedicated power wire (fused) from the battery for the camera relay. It takes 5 minutes to run the wire from the battery to the trunk.