Not sure about the harness but when i had my 02 botemate trailer i had lighting problems as well. I tied on to the existing wires and fished all new ones in. The old ones had no insulation left and kept shorting out. If that does not work you can use a shop vac at one side and tie on a string and small plastic bag on the other and suck new strings in for cable replacement. The dedicated grounds can go to a common point on the harness side and all the other light grounds just go to bare metal on the trailer. The trailers body will carry the grounds throughout as it is all one metal structure. Hope this helps.
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2002 outback lsv 320 tbi
02 f 150 supercrew lariat