A lot of it contradicts its self so using the last diagram from l84sky. the tail light pin would supply the tail lights on both sides, the side lights and number plate lights run off of the same pin as all 6 lights run at the same time. The amber and red unit on the board below houses the: tail light (which appears dim through the red lens when on),The fact that the existing trailer lights and the new "board" work on your friends truck, but not on yours suggests either a compatibility problem or incorrect wiring - I suspect the trailer ground may be wired to the side-light circuit - this diagnoses by the way, is based on the diagram that L84sky provided, if the previous owner did his own thing, which is entirely possible, given the load of black wires you describe, then you might need to get an auto-electrician involved.
Something I want to point out here - this is an international forum, and different countries may use different terms to describe the same thing, and this is what leads to the confusion I alluded to earlier - what do you call side lights, and how are these different from rear lights?
Maybe a picture of the "light board" with notes as to which lights do what would help clear things up.
Yea I definitely dont have the 6 pin, sorry picture isnt clear phone doesnt like the flash