Hi again Khoder.
From what you've said in above response you've got the third connection correct (Light Blue from body harness connected to yellow from trailer harness).
I've checked my trailer harness and can verify the following for you:-
. GMH Part number is 92144494 (there is a label attached just near the end of the yellow wire which, by the way, has red squares dotted along it);
. There is a grey coloured cable (about half the thickness of the other cables) coming out of the trailer wiring loom and it has a black plastic single female connector attached to it. This is the one that should plug into the white lead (with the black plastic male connector) from the body harness.
. Definitely the body wiring harness wires coloured Black, Black with Blue tracer, and Light Green (each of them with single connectors) should each be not connected to any other wires.
The Lumen 7 pin flat socket which is fitted to the trailer wiring harness actually has 9 connector points inside the screwed-on cover (where the wiring connection is done - not where the trailer coupling plugs into under the hinged cover flap). The additional two connection points are wired one with the grey wire (next to the green wire) and the other has a siamesed connection to the white wire (comes from between the black and the blue wires). Reason for the extra two connections is to connect the Lumen plug's internal reed switch to the wiring harness to give a signal to the BCM that a trailer is connected and hence don't send reverse alarm signals because a trailer is attached. Otherwise you'd get the alarm beeping whenever you engaged reverse with a trailer attached.
I think it may be beneficial for you to have a close look for the thin grey wire coming out of the trailer loom and connect it to the white lead from the body loom (and, of course, to leave unplugged the black and the light green and the black with blue tracer).
Hope this helps get it all working as it should.