In this picture, I can clearly see that the solenoid is connected to what looks like a flasher box, that you describe as being a "junction" box located just behind the left headlight.
Looking at this, all that I can assume is that the black wire going to the terminal next to the fuse, is getting power to if from somewhere in the front of the car, and then is transferring that power via the black wire to the large terminal on the solenoid. Both of these wires are positive (+) wire, or what might be called "hot" wires. This is where it gets really confusing, since the other side of the solenoid has no wires attached to it, so the solenoid isn't doing anything. It also appears to be a solid piece of copper wire, which wouldn't have been used by the body builder, since that is house wire, not automotive grade. I can tell this because of the fact that it is elevated and appears to be very stiff. This indicates that the person that installed this wire had no idea what they were doing. What also brings me to this conclusion is that there is a circuit breaker protecting the positive wire between the relay that is mounted on the fire wall and the solenoid. This should have been a fuse, not a circuit breaker, which would reset once it cooled. In my opinion, this is like having a lit match next to gasoline. It is a recipe for disaster. Presently, the circuit breaker is lying on the windshield washer bottle. In essence, you could remove the solenoid, and the associated wiring, since it isn't powering anything.
The black wire that has the yellow insulating ring at the end of the terminal is my next concern. Where does this wire go, and what is it hooked up to. Once that is determined, I might be able to further assist you. Above, I made the assumption that this is a hot wire, but I cannot be certain. It might be powering something else.
What you are calling a "junction" box, looks very much like a Dietz flasher box, and if it is, then the power comes into it on the black wire (with the yellow ring), and two of the other wires that are pictured, each would go to a light bulb somewhere on the car. The 3rd wire, I will assume is a ground, but without a better picture, and knowing where each of those wires go to, it can't be said for certain.