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Hello I will help you with your question,
Is there any evidence this car has been rebuilt or in a flood?
Are you able to remove the lamps and check for power to the lamp socket?
Sorry I was offline for the night when you replied
The way this circuit works is the lever moves the switch which tells the engine computer that you are in reverse. The computer puts that information out on the communication buss and the smart junction block closes a relay which sends power to the lights.
You can check fuse #29 in the smart junction block to see that it does have power with the key in the run or start position. If it does then the fault could be in the switch, or the smart junction block. If you have power at the fuse then a scantool capable of reading the switch state would be necessary to check the rest of the communication.
Please let me know what you find and how I can help