What was described in the initial post is a rear end wobble...not a lurch, not a drift, not a pull and not a vibration. However, as systems go, all could be ... or not be part of the resulting root cause. Not sure at all about the leaking coolant reply that came out of left field...certainly not anything I would consider based on my 50 years of wrenching. In my opinion, the pan-hard bar reply is dead on, but.......
The death wobble. Comes in two flavors...front and rear. Both can be caused by several problems that result in the same symptom, but is mostly a symptom of rigid axle suspension designs that are loose.
Out of necessity, I've been following this symptom on several boards now for almost two years and it seems very few real answers are out there. Lots of guessing tho. My one 4Runner was used in my business for 5 years towing trailers near the upper limit of the truck's design. Subsequently, the wobble showed up and got worse. And then worse. A death wobble.
Here's my take on getting to the real, no guesswork needed, solution: First put the truck in the air and inspect everything in the suspension with a very good, bright flashlight. Look for leaks in shocks (replace them in pairs), crushed or split bushings (replace), broken stab link ends (replace them in pairs with urethane bushings also), broken springs (duh). Check for broken mounts. Find a good frame shop with welder. Check tie rods for play (replace). Check wheel bearings for play (they don't always groan when bad). Check your ball joints with a pry bar the correct way now that the truck is up in the air. Uppers and lowers. Replace with OE or Moog.
If your shocks are more than 60K miles old, replace them unless you've only driven on smooth highways at highway speeds and don't brake hard or accelerate hard. They may last another 20K. Naturally, fix any other problems that you discover from the visual like rear heater coolant leaks
.
If you have discovered more than one problem during this first inspection, fix them all at once. After that, only do one fix at a time. Plan on spending both money and time whether you do this yourself or direct your mechanic on what you want them to do and how you want them to do it.
Now that you've taken care of the obvious, go for a ride. If there's vibration you have to locate it. If it's in your seat, or your hands only, then move the front wheels to the rear and the rears to the front. If the vibration moved, it's in your wheels. Get them balanced with a road force balancer.
If no change when you move the wheels, then check your drive-line for bad u-joints and have it rebalanced by a reputable shop. However, a bad drive-line will not create a death wobble and you will usually always feel it in your seat only.
Now that everything else is taken care of, down to the death wobble. In my experience, a front wobble is rare in any Toyota and I'd eliminate the rear first. Note that since no one, and I mean no one is making poly bushings for the rear of a third gen 4Runner, this can get ugly. Pull the pan-hard bar (lateral track bar). Inspect the bushings at both ends for distortion (an area of crush parallel to the bar itself is common), as well as dry rot and excessive cracking. Any of these....replace the bar. ($200) If you are handy, you might be able to take a universal poly bushing from energy suspension, daystar etc and trim to fit on a lathe. Mine had high hat rubber bushings from the factory, so washers were necessary to shim the bar correctly since no two piece high hats were out there when I looked. Replace the bolts with new, no matter what. The bolts take a beating, they wear and get 'loose'. If you have 1/32 inch play at one end, you have it at the other also and it's cumulative in effect. The wobble should disappear on the next test drive.
IF not, then it's on to the lower control arms! 4Runners that do a lot of towing will show a symptom upon acceleration and deceleration where the front of the truck seems to 'steer' in one direction (to the right when accelerating) and then the opposite when letting off the gas. Once they hit 200k miles, the same. Heavy acceleration or supercharger abuse....control arm issues. The axle is moving forward and rearward on the drive side which means...Lower control arm bushings are shot. Like the bar, no one makes a Gen 3 urethane replacement. Toyota has the rubber OE, part number 48702-35070. Most parts guys will tell you they don't exist...or that they are only for one end. Not true and not true. Toyota OE control arms are anywhere from $137 to list price ($212) each. This is what they try to sell you. Ouch. Careful if you go to your local pick-a-part because you most likely get the same or worse condition. Many yards move their wrecks with forklifts and the lower arms take the hit. In my opinion, you may only have to replace the bushings on the dog bone that attaches to the axle. Replace both and test drive. If I'm wrong, replace the other two after the test drive fails. You might save a few bucks. Replacing the bushings is a shop job. I mean, you need a really good, 20 ton minimum press and adapters that fit what you're trying to accomplish. The bushings are 44 millimeters in diameter and you need something that will press that outer shell/ring without damaging the center that projects out from the bushing. I used an old motorcycle piston turned on a lathe and the center drilled out to fit.
These lower control arms are mostly to keep the axle perpendicular to the center line of the frame, whereas the pan-hard is to keep the axle centered left to right under the frame. If there's enough slop in these lower arms, the axle wanders. The upper arms are for resistance to the rotation forces that can cause the axle to twist forward or backward. These will be the last to go since this force is minimal. But they do go.
If you have done all of the above and still have the wobble you either missed something, or you have a broken frame or component mount (you missed something). Time for a new truck?