The most common cause of backup lights not working is a blown fuse or a bad backup light switch on your Motorhome’s transmission.
Some other causes can be a bad ground, shorted wires, the bulbs being bad (use a 12 Volt Circuit Tester to see if you are getting power to the backup lights while the RV is in reverse, if you have power then replace the bulbs).
Another problem is if the RV was stored outside for a while it could be that some little critters have gotten to the wiring and chewed through some of it. You may have to trace the wiring to look for critter damage or other damage to the wiring.
Without actually being there it is hard for me to really get to the root of your problem.
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