1998 Toyota Camry Reverse lights

The symptoms are typical of a bad ground. One circuit, when turned on, back-feeds through a different one, in this case, the backup lights and indicator. You should find other rear lights aren't working properly either. Usually that means the brake or tail lights are not full brightness. Follow the wires from one of the backup lamp sockets to see if it is cut or the terminal that's bolted to the body is loose or rusty.