Here's THE explanation of this form of what has been called 'shimmy' long before many of you were born. Keep in mind, I have over 40 years of automotive engineering in the Vehicle Dynamics realm, and have even worked on hybrid specialty vehicles (limosines) that you might see on TV in National News reports that needed this problem addressed.
'Shimmy' is the unintended result of coupling between vertical wheel movement and wheel steer movement (not steering wheel movement). The root cause is non-zero angle on the single or double tierod(s) connecting the Pitman arm to the tie rod connection(s). If the tierods are not horizontal in the front view, your front suspension is susceptible to shimmy. A vertical wheel displacement (bump or pothole or tire imbalance) excites lateral forces in the steered wheels mechanism. Much like an inverted pendulum, the oscillation grows because of positive feedback from the steer mode to the vertical mode of wheel travel. Like any pendulum system (hinged from the top or bottom, techniques to reduce or eliminate it involved damping from either friction (new suspension parts) or dampers (steering shock absorbers), or removal of the coupling factor. Obviously lift kits that do not re-align the Pitman arm are principle players. 'Bulldozed' springs which lower the body also are involved. Bulldozed springs are deformed (as in bent) usually from overloading due to many situations. This aggravates the coupling term. Additionally, vehicles with power steering can have worse shimmy because the flow valve in the steering gear will respond to the increased tierod loads in an attempt to reduce them, but with a phase delay that actually increases the forces. Worn steering system parts (lower friction), worn-out pump, lower rack&pinion slipper bearing friction, valve leakage, play in ball joints all add up to create the shimmy phenomenon.
Tires are also players because the air pressure, tread width, wheel rim width and sidewall stiffness of the tire carcass affect the steered stiffness of the tire (called self-aligning torque stiffness). So tire brand, wheels and pressure are ways to reduce the problem or make it worse. Sure, steer dampers help to reduce the amplitude of the shimmy, but eventually these parts wear out or get damaged from the high forces and soon the problem returns. But the root cause is the positive feedback in the steering mechanism.
Note that many of these trucks have symmetric ride steer. (both wheel turn the same way when the front end rises. In most vehicles with purely independent suspensions, the wheels turn in opposite directions when you raise the front end up. (called ride-toe or bump steer). This parallel steering design also feeds the problem because both tires scrub the same way instead of one tire cancelling out the other's steering resistance moment. Note that many different Pitman arm drop dimensions are available from truck specialty shops which correct the geometry factor of this problem. Steering gear stays put, steer arm ball height is altered as installed. But the loss of friction from wear/mileage is always going to aggravate the situation. Plus, soft springs means lots of wheel travel, so the Pitman arm can't always be horizontal.
Now you know the reason(s), many science projects and technical papers written about the subject, but the lore from owners with 'feelings' instead of facts & data permeates the web.