1993 Jeep Cherokee Sport, love the silly thing...
It had the front-end death wobble, replaced (almost everything) and got that fixed, much better.
However...when running on Colorado's roads (similar to dirt roads in smoothness, but are paved with lots of big holes and wide ruts in them) above 50 MPH, I get a similar-to-deathwobble-sensation, but from the REAR of the Jeep, not the front.
Things I've done to chase it: when I replaced all the bushings and other parts in the front, I also installed new bushings in the rear's swaybar mounts. This Jeep has the leaf springs in the back, with recent shocks (8 years old, but only about 10k miles at most on them) like on the front: good shocks.

The only thing I can think of that might be left to change is the rubber/elastomer mounting gizmos in the leaf springs themselves, but I've never seen these cause a problem in my [many] other cars, like station wagons, Lincoln Towncar, or (1960s) full-size Fords. Can they cause such severe rear wobbles in a Jeep?

About 50% of the time the Jeep will rear-wobble momentarily when passing thru 50 MPH to 65 MPH, then settle down, but if there is a strong sidewind (typical in Colorado) like 40+ MPH the wobble at the back never quits.

Got any good, experienced ideas about this one? It seems rear wobble is rare, at least in the all-wise Internet...

 

Don't know about the "good, experienced" part but how are the rear springs? They are over ,30 years old if original. If your problem is really in the back I'd suspect the springs are sacked, the bushings are shot, the bolts are broken, or the shocks are shot, first suspect being the springs

or you're actually driving a very old VW bus

 

Check your "C" clips in the rear pumpkin. If they are worn sometimes they can break or drop out and out come the axles or work back and forth. Rare but have seen it happen twice.

 

I ordered up some of the rubber bushings in the ends of those leaf springs, and their hangar brackets at the rear ends. In all the years of having 1960s cars I never saw any of them have troubles with leaf springs (I didn't have GMs, only Fords) but I know that GMs of many types had those flat slim spring plates in their leaf springs, which you could find by the handful if you walked the side of the road almost anywhere. I'll be back after I get them (and install them) to see if they help: I've not seen it help (nor change anything) on any of the 1960s-1970s era cars, though?

 

I did this back when I first got this little Jeep: I went through the differentials at both ends. They got new oil then, too, and seals, just in case: they had no issues that I could see. That was when I discovered that I could see carpeting when I looked up from under the car: then I had to install a whole new floor, as the aluminum one was destroyed by the salts they use here on the roads. We get LOTS of snow in a normal year - this one being a rare (and very strange) no-snow (nor cold) winter, so far. We've only had 2 little snows (6" and 12") since September, weird...

 

Check wheel weights
Check for mud in the wheel
Check tire for bulges
Tighten lugnuts

I've seen all four of those cause rear end issues, none of which were obvious until they were found.