Something isn't right with the testing...
The power going to the 7-wire plug/harness is 12v
DC only. There should be absolutely no 120v AC on the 7-wire hardness.
Coming from the tow vehicle, there should be the following in the 7-wire harness:
- Electric brakes
- Left turn/left brake light
- Right turn/right brake light
- Tail lights & marker lights
- Reverse lights (not on all trailers)
The color of the wires will vary from year to year and even trailer to trailer. The position of the wires in the plugs is pretty much standard, and the exact layout should be in your manual.
To test the lights on the trailer, you need a 12v DC power source, like a 12v battery. Connect the negative of the battery to the pin which is shown as 12v negative in your manual's diagram, and then connect the 12v positive to the lighting circuits one at a time to see what lights up.
If you're getting things crossing over from one to another, my guess is that either a) your 7-wire harness cable was crushed or cut at some point in time and is shorting, or b) the junction point where the trailer's wiring connects to the 7-wire harness has been compromised.
If both of these areas are okay, then you've got a short elsewhere if the lights are cross firing.