The shape of the male ends are different than your old ones and what I am familiar with. Make sure all the lights are off, and test the single (ground) side of the right harness into one female end on the truck to see if it fits and you get a good metal on metal contact. If so, then you can just cut off the plastic/rubber and go from there.
I wired my utility trailer with new LED light set from Harbor Freight, twice. First, I got the rectangle submersible set. They were too wide and ended up breaking one. The other had grounding issues. So I got the square set and re-ran all the wires including a ground wire. All good now. I don't remember now what the harness looks like now. I did not cut any cover on the harness, though.
Don't worry about mis-wiring. The truck has fuses in case you screw up!