2004 Ford F-150 Rear end shimmy/vibration

The rear end starts to shimmy/vibrate whether in 2 wheel drive or 4 wheel high. The shimmy comes and goes. I have all new tires(factory specs). This truck has the 9.75 rear end with 3.73 gears and limited slip.
Where do you think there is a problem: u -joint, brake caliper hanging up, wheel bearing going out, limited slip clutch pac not engaging/disengaging, ?
Again, this substantial vibration mysteriously comes and goes. No signs of leaks anywhere. I am stumped. Thanks for your ideas.