Q: Reverse lights stopped working.

I replaced my engine battery in my hybrid car. There was an issue getting the battery out, as it appeared to be the original battery that came with the car in 2006. Shortly after the replacement, I noticed my reverse lights stopped working. I checked the bulbs, they were fine. Checked the fuses, they were fine. My friend thinks it might be the relay box. Which of course is a more expensive repair. My brake lights are fine, except one has gone out, but we believe it is the bulb.

I am wondering if anyone has ever heard of such a thing happening with the hybrids? I do know certain types of repairs have to be done a little differently due to the hybrid nature of the vehicle.

My car has 139000 miles.
My car has an automatic transmission.