sjb-Are you absolutely sure you have power to the plug? If the tow rig is a GM product with the factory installed trailer wiring you'll likely have separate fuses for running lights.
You know what, I will double check. But I did check all the fuses for trailer lights and did take my handy dandy little tester to the female end of the pigtail on the truck and the trailer light plug lite up both on the 7 pin harness and my 4 pin. So I am pretty sure.
Now that I think of it, I also took a 12 volt gel cell and connected that to the 7 pin male end. I could get the brake lights to light up no issue. But nothing but a small spark from the running lights.
Frustrating.