I would not wire anything directly to OEM equipment. It can cause other problems down the road.
For my reverse sensors, I have a relay in-line at the reverse switch on the shifter mount plate. When the shifter is in reverse, it energies the relay, turning the system on. Power is isolated so I don't have to worry about blowing fuses.
Same for your application. Put a relay in-line on the orange (hot) wire. Then you can run a separate power line dedicated for the camera and not worry about potentially blowing fuses or bulbs. Standard automotive replays are dirt cheap and protect the OEM equipment.
If you are not 100% sure which wire is hot, buy a tester. Again, these are dirt cheap and make finding the right wire easier.
Black wires or black striped wires are generally ground, but not always. A tester will confirm.