If you can find the proper diode then that would be the simplest, diode acts as a one way gate, power can flow from the backup lights to kick the relay for the lights, the diode would prevent the power from the manual switch from going back to the factory backup light circuit.
or
Wire up the circuit like normal using a switch to kick a relay to power the lights, then run a second circuit with a 2nd relay, use the back up light circuit to kick the 2nd relay/circuit.