Brake lights and tail lights don't work

A broken ground wire is a good suspect, especially if there's a trailer wiring harness and someone made the connections with connectors that don't seal out moisture. Start by testing for voltage on the terminals in the sockets while the tail lights are turned on. If you find voltage on one terminal in each socket on each side, put the bulb in, then test for voltage on the brass base. If you find voltage there, the ground wire is open.