Do you know how to use relays? One way although others may say there is an easier way is to use two relays. Fused power (for the aux backup light) to the common on the relay. Maybe use the same line to the common on both relays. The normally open contact on the relay then out to the lights, again tie them together. Now the other part, Ground one side of each of those coils on the relays. On one of the relays, tie into the hot wire feeding your stock back up lights. On the other coil, tap into a fused and switched power like your cigarette lighter put a switch on this line.
Each relay is in parallel and then you have two methods to turn on your aux lights. And the best part is if you use a switched power for the second relay, you can't accidentally leave them on and drain your battery.
Re-reading your post, you can do that with one relay, just put a switch on the circuit with the power to the coil coming from your reverse light. This way the relay will start the aux light every time you are in reverse but if you flip the switch on the relay, they will shut down.
