[Lynn Eades]

Many types of 4 wheel drives can suffer from this. To eliminate the problem requires that all aspects of the front end are up to spec.after an initial general check, I would check the king pin preload (as previously suggested) Every thing helps to either eliminate or compound the problem. Things like lateral float at spring shackles, spring set (loss of castor) a slightly grabbing brake. Tyre, wheel, brake drum balance, out of round, wheel bearing play, any aspect of a tyre (off set in mold?)that is not perfect is detrimental. (some tyres will go out of round when parked with a load on them, and will not come right until they are once again warm from driving)

If the truck has Timken taper rollers as king pin bearings (Dodge used bronze upper cones in a Timken cup (I suspect they had condensation problems rusting the upper cones) they wear in one place becoming loose in the straight ahead position. Correct preload causes a somewhat alarming distortion of the housing but they then drive well (assuming everything else is good as mentioned previous posts)
Another possibility is the state of the universal joint in the front half shafts, and also the centering of the joint on the king pin axis line (shimmed in a jeep, depending on axle joint type)

Any one of these things can help to set off this shimmy.
Hope this is food for thought.