One of the culprits in bump steer is the drag link (sometimes called the steering connecting rod). Ideally it should be parallel to the ground...parallel meaning parallel from the pitman arm to the steering arm. The reason? Because if you imagine a circle with a dot at 90 degrees, moving in an arc from that 90 degree point up or down a bit will produce a smaller motion at the steering arm than a dot at say 75 degrees or a dot at 115 degrees. Let's look at a crude drawing I made below...click on it and hopefully it will get larger. The red oval shows what happens if your bar is parallel. Movements up/down cause a deflection, but you can see it is a small one. Now look at the arc of the circle inside the green and blue ovals. It changes and gets larger. The end of your drag link is following around that circle by definition. And even a bit of movement up/down moves the end of your drag link further in or out if you aren't parallel...and this is part of what is causing your truck to steer itself every time it hits a bump.
First I'd suggest going out to see how far from parallel to the ground your drag link is. You may be surprised. You may also be surprised to know GM knew your drag link wouldn't be parallel. Take a look at the second image. That is from the Shop Manual covering your truck. In the upper corner, you can see GM drew the drag link at an upward sloping angle of about 75 degrees or 15 degrees off of parallel. And in the suggestion section, GM doesn't mention "make certain your drag link is parallel with the ground."
Next I'd suggest considering purchasing a sway bar. This will tug on the opposite end of your axle whenever one end is pulled up or pushed down, making sure each side reacts to a bump in relatively the same way. The sway bar's main function is to reduce body roll when you're going around curves, but in the case of a straight axle it can help with other handling issues.
And of course do all the things mentioned earlier...the more "like new" your steering/suspension is, the better it will work.
Good luck.
~ Jon 1952 1/2 ton with 1959 235 | T5 with 3.07 rear end
