I step on the brakes and the reverse lights also come on. What's going on? How or what can be fixed.

 

Sounds like it might be a short or bad grund at the tailights between the reverse and brake bulb wiring...maybe pinched wires, but more likely water in the tailight housing casuing corrosion and/or a bad ground causing the brake bulb to find ground through the reverse bulb. Gonna have to open up the tailight housings and check the connections.

 

I'd investigate for a short as well. Could be a chaffed wire somewhere in there. Start simple, check the obvious stuff - connections & bulbs to rule them out. Then get OCD on the wires.

 

^^what they said^^