A severe shake is a good reason to look at all the front end wear items. Don't assume or guess.
The pitman arm ends and tie rod ends should have no more than 1/16" play. The pitman arm to steering gear output shaft bolt should be tight with no play (very rare but serious)
The steering gear should be tightly bolted to the frame and the area around it should be cleaned of any crud or rustproofing and checked for stress cracks. These cracks are common enough that there are a number of aftermarket kits to repair or prevent the cracks.
The "rag joint" in the steering column should be checked. It's the rubber impregnated fabric joint. Grasp each side of the shaft and, with the engine OFF and the steering column unlocked, have Soldier B gently move the steering wheel side to side. There should be no play. Slop in the bolt holes is more common than an outright tear.
Check the shocks. If they are OEM, replace them (they are over 20 years old). If there is any leakage, replace them. Pick up and push down on each front corner and get the truck bouncing, then stop. The truck should stop moving in just a single oscillation or two max. If the rubber bolt bushings are shot (the bolt will be off center), replace them.
Check the steering damper. Have Soldier B turn the steering from lock to lock, observe how far the damper travels. Unbolt one end and run it through that range of motion. There should be uniform firm resistance and no hesitation or jerkiness. It should not want to exhibit a "memory" and return to any single length. When you stop pushing or pulling it should rest right there. There should be no leakage.
While each wheel is jacked up, look for bearing play by grasping the outer edge of the tire with a hand at 12 and one at 6 o'clock. Push with one hand, pull with the other and alternate. There should be no more than barely perceptible play.
Check the connections between the springs and the frame and axle.
Look at each end of the springs. The bolt should be centered in the eye of the bushing. If not, replace the bushings or springs.
If all this checks out and the play is still there, check the kingpins. The king pins themselves rarely need replaced. There is a sacrificial bushing above the upper king pin that is under significant spring pressure and it's the most likely wear item. Unless the kingpin is badly pitted or visibly worn out of shape, it won't need replaced.
Steering dampers cannot cause front end shaking so they cannot fix it either. All they do is damp road shock to reduce stress on the front end parts and to help keep the vehicle going where the operator wants it to go. If anyone has had a front end shake "fixed" by replacing a damper, especially by up-sizing one, the worn or out of adjustment parts are still there. They are just masked by the damper.
Good luck
Lance