No Brake Lights in Reverse (WANTED)

Is there a way to alter relays so my brake lights do not turn on while in reverse?

ISSUE:
I have a backup camera, mounted above my 3rd brake light, on my camper shell. View wasn't an issue until I finally wired up the 3rd brake light. Now when it's night, the light drowns out the camera since they are so close togther. I could move the camera, yes, but I like the high mount so I can see my boat while towing, and it's just a better view. I could wire a disconnect switch so I can cut power to the 3rd when I'm backing up, but that's why I want to alter the harness/relays/etc. If it's too complicated, I might just disconnect the brake light!

Thoughts?

Also, since I wired the backup camera to a switch, I can manually turn the camera on (which is displayed on a Kenwood unit) by sending power to it. In turn, it turns my reverse lights on too. Not an issue, but the issue is it throws a transmission error (only sometimes... it isn't a matter of speed or length of time on... weird). If anyone can recommend a way to alleviate this issue, that'd be great!!