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would be good to check all the steering connections to make sure they don't have a lot of extra slack. also the tire(s) may be out of balance causing that shake. my p/s pump is going out and i've got a semblance of a shake there. may check that as well.
Is there a lot of "slack" in the steering while driving? Does it pull to one side or happen more/less when you apply the brakes? Do you hear any noises while turning?
Also, check both front tires carefully for anything unusual, like a bulge, there's a remote possibility it could be a broken cord.
Is this like an all the time thing or just under certain conditions?
Is your truck a 4x4 or two wheel drive?
Tires that have a bad wear pattern from a bad alignment.
Tires out of balance
Tires with a defect like broken cords, knots, chunks missing.
Tie rod wear.
Ball joint wear.
The tires are newish and the brakes are good. The steering wheel has slack in the upper half just below the shifter. The lower half of the column is solid bolted to the truck, no shake there.
I just can't figure out looking at the column how to get into it to replace shims or tighten something up.