Thank you Rodney for bringing up this thread again as I am having the same type issue. It was really noticeable coming through the mountains of Kentucky on the way home from Wisconsin. Now, it does it when the brakes get hot, under the load of the fifth wheel only. Not car trailers loaded, but the fiver. No pulsating pedal or any other type of vibration when not towing no matter how hot the brakes get.
I just came in from tearing my rear brakes apart thinking I would see something like a stuck slide pin, but nothing. Pins are slick and move freely, all pads wearing evenly, rotors are not scored, so I have no idea. The shimmy starts in the rear of the truck and feels as if it progresses forward. The Bilstein 5100 steering stabilizer stopped a lot of the steering wheel vibration when it starts. Other than slightly warped rotors, I don't have a clue!!

 

Mine does it too Monty. Only with the trailer also.................I need to check rear brakes yet but nothing stuck on fronts.

 

 

Check the brakes on the trailer. They should be good enough to stop the trailer. Sounds like the truck is doing all the work.