I don't know what "distribution strip" means either. My trailer has a 7-way connection point on the trailer that the umbilical cord plugs into. My cord has a plug on both ends and is reversible. My tow vehicle has a 7-way connection point. All 7 wires are used.
My trucks 7-way connectors are wired to standard 7-way profile. I test all of the three components with a 7-way tester that I got at the auto store for about $10.
I wire the trailer to agree with the 7-way tester. I wire the cord to agree with the standard 7-way profile at both ends. I ignore all wire colors and only wire to function. Standard 7-way profile is based on function, not wire color. My tools are the 7-way tester, a 12 volt
jumper light, and a small 12 volt
I test the tow vehicle with the 7-way tester to be sure it's right. Then I use the 7-way tester to test the trailer 7-way connection point, and to test the removed cord . . . all separately. When everything tests okay, then I plug the tow vehicle into the trailer. I do not have to hitch with the ball hitch to test the lights, there's a common ground.
I didn't like the trailer ground setup so I brought all the ground leads together, fluxed them with paste flux like I was going to solder a copper pipe, and soldered them and the new #10 ground lead together with my map gas torch. Then I soldered a copper battery cable eye end to the new lead, sanded the skin and screwed the new lead to the trailer skin.
When I tested my system I had two wires reversed on the removable end of the umbilical cord.
There's one thing to watch for when looking at function and wires. The tow vehicle brakes and the brake lights look a lot the same until those are isolated and objectively tested. Towing would not be a good way to test those.
Edit: Glad you got it fixed. I'll leave the post up for others.