With the transmission in Park, verify the rear camera is on and the reverse lights are illuminated. (That ought to make the driver behind you nervous at a stop light.) If both are enabled, you may have a bad Reverse switch.
When shifting into Reverse, verify the gauge cluster displays the Reverse selection., that may be another helpful symptom.
- I've removed but haven't taken this shift assembly apart, but there is an electrical connector attached to it that has more wires than those needed just to illuminate the shift indicator bezel (it also reports transmission gear selection to the Gauge Cluster.) The good news is, if the switch is bad, the assembly is cheap.
There is a mythical CUE "reset" procedure that has been posted over the years. Even the CUE Guru at my dealership was aware of it. So I said, "Humor me and perform it." He tried. He failed.
To properly reset the CUE system, removing and re-applying primary power works consistently.
Yours is an interesting problem, (could be hardware or software) not previously reported. The software that controls the transfer from the infotainment screens switches the display to the camera feed full time, and the BCM (Body Control Module) which controls the lighting fails to activate the reverse lights. That's why I was hoping you would report the reverse lights were enabled, which would suggest the problem was transmission lever-related. The BCM may be suspect. I've gone through the current Cadillac TSBs (Technical Service Bulletins) and none match these symptoms.
When you get it resolved, please report back and post the cause.