One of two culprits:
1 - the back-up bypass valve is dysfunctional
2 - the electrical feed from the backup lights circuit to the bypass valve is dead
The valve bypasses the brake fluid from the line to the calipers back into the reservoir allowing the master cylinder to compress without actuating the brakes. So, either it is not working (bound up or corroded) or the electrical circuit is not complete to actuate it. Make sure the WHITE ground wire is making good connection, don't rely on just the hitch to make that connection.