Ok, perhaps then the lights are wired into a circuit that is only powered when the engine is turning. Next thought since it happened when you shifted into reverse would be to look for a safety switch somewhere on the shift linkage to the transmission. Make sure a plug or wire has not come loose on it.
Also not to sound demeaning but make sure you have the PTO off, shifter in neutral, and parking brake set or whatever else you normally need to do when starting it up. (I've admittedly missed doing two of the above myself during the brain fog of frustration
If still no joy, from there your best bet would be to get a volt-ohm meter and start tracing wires and better yet have an electrical diagram in hand. In addition to a failed safety switch somewhere it might be there is a relay that is triggered by the safety switches that has stuck or failed.
Using your model and serial number you might
be able to download a manual with an electrical diagram at the link below:
PDF Manual Web Archive