I also have the B&W hitch, and bought the Ford factory bed plug. You'll be surprised at the shape hole it requires from the factory! NO Holesaw shaped like that,,,
I plan on cutting the tabs off the plug, just drilling three holes, one for the recessed part, and two for the mounting point. It will plug straight into the factory harness, at least that's what the parts guy said. (I do NOT have 36" of wire with mine. At most it goes 18-24" or so out from the plug itself.
I hope to install mine tomorrow if I have time.