Death wobble comes from slop in steering or suspension components. When an outsides force jostles the tires they begin to oscillate without input from the steering. Usually input from the steering will not stop it. Sometimes abrupt acceleration or slowing can stop it. It is an odd feeling when your truck starts bucking or shaking and you can't get it to stop. While a rear leaf bushing can cause clunks and other handling quarks, death wobble will not be one of them. Brian's suggestion about looking for slop is a good suggestion. Be patient, something is likely worn. Tre, trac bar bushings, old hiems, control arm bushings, steering box/rag joint/ shaft, wobbled out trac bar mounts, ball joints, loose trac bar bolts, etc. I have even seen it happen with a weak/ flexing trac bar upper mount.
Ricks suggestion about toe in is a good one. With 37s, as much as a 1/4" is good.
Also as light as our rigs are, I only run 23 or so lbs in the tires all the time. They ride so much better and the tires wear out evenly middle/ outside. That can calm handling quirks as well.
On jeeps, the drag link is connected to the passenger knuckle and the tierod is connected to the drag link about a foot above the knuckle. The axle is far forward compared to the steering box so the drag link is Curved to clear mounts. All of this puts a ton of stress
On the steering linkage and causes toe in to change through suspension cycle. Jeeps run a steering stabilizer which can usually control/ mask worn parts and keep them from causing/ allowing death wobble. It shouldn't be necessary on a 1 ton Chevy setup, but could be installed if the problem persists. I would only do that as a last resort.
