Again more progress, we are getting somewhere! Picture #1 the bulb socket in your hand is for a dual element bulb. The low wattage element is the tail lights, the high wattage element is for the brake light and if there is no separate yellow lens the turn signal/ hazard light. One of the terminals in the socket will have power when the running lights are turned on and the other will have power when the brake is activated, intermittently when the turn signal is on or the hazard flashers are working so neither of them are grounds. The bulb is grounded when the pins and metal case that hold the glass part of the bulb on is installed in the metal part of the socket. You should have 3 wires coming out the back, one ground attached to the metal housing in the bulb socket and two powered wires going to the insulated pins in the bottom part of the socket that complete the circuits for the brake and tail lights when the bulb is installed. Place the red probe on the inside of the bulb socket against the outside metal part while the black lead is connected to the shinny metal frame and check continuity , it should be connected and sound. Be sure to let us know what you find. Picture #2 the white wire screwed into the frame is probably the ground for your trailer plug and looks to be rusty metal. Make sure there is shiny metal under the terminal and continuity between the plug terminal and you clip on the shiny metal frame. The large black wire loom that is tucked up in the frame just behind your clip is probably what we want to follow there should be power and ground wires for all the rear lights inside it and some where nearby there will be a ground or several ground wires the exit the loom and are attached to the frame (that is where I believe we will find a problem) as your frame appears to have severe rust. There is a green wire there loosely strung that is probably a brake light wire that has bee spliced into a brake light circuit that will also go to your trailer plug. Picture #3 looks like you did a good job with your test lead, to test it put your meter on continuity and touch the red lead to the clip on the frame, it should sound.