Seems possible to me, all you would need to do is use the power to the reverse lamps or the reverse lamp pin on the 7 pin trailer connector. Run that power to a 4 pin relay coil side. So that no power is robbed from the reverse circuit. Then power the relay from the battery on a in line fused wire. Once the relay is energized by the reverse lamps, the relay will then power the light and actuator.
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