I have not been able to Source a diagram for the fuse box in the engine bay.

My trailer signals and brake lights work, but I have no running lights.

I seen talk with the older QX56 and Armada having an F for fuse that needs replaced for running lights, but I can't figure anything out for the 2011 QX.

Can somebody please help? I just bought the vehicle and I have a road trip shortly.

I always thought the diagrams were either on top of the fuse box cover, or on the inside once you remove it. Anyway, try looking in the FSM:
https://www.nicoclub.com/FSM/QX56/2011/
Perhaps in the PG section?
https://www.nicoclub.com/FSM/QX56/2011/PG.pdf

Went through 166 pages of PG. nothing.

Inside fuse box cover has diagram. Underhood cover does not.

there should be a routing diagram on the inside. but since you dont see it, did you test the wiring at the back of the car where you plug in the trailer harness? are you sure the harness has continuity?