If the whole column is moving follow the column from the steering wheel down to the firewall. You should find one or two brackets designed to hold the column in place. The bolts on the brackets may have worked loose. If the movement is inside the column shell I would strongly urge you to seek professional help immediately as this not an area for a beginner. Hope this helps. Ralph
There are 4 screws at the base of the steering column that typically come loose. Disassembly of the steering column is necessary.
1st - Remove the steering wheel by loosening the nut under the horn button; then use a steering wheel puller to pull the steering wheel off of the splined hub.
2nd - Remove the steering wheel lock plate by using the lock plate puller tool to press the lock plate down; then remove the retaining ring.
3rd - Carefully remove the turn signal cancel cam; turn signal switch; key switch and plastic collar.
4th - Remove the steering column pivot pins. There is a special too for this job.
5th - You should now have access to the 4 loose bolts. They use an external torx head. Remove the bolts, one by one; apply threadlocker to the threads, then reinstall bolts.
This is the basic run down (from memory) of the job, there may be some additional (simple) steps. A good tech can knock one out in under 45 mins, however, if this is your first one; take your time and allow several hours for this job.
This problem does not only affect c/k trucks. Any GM vehicle with tilt wheel during the 80s through the mid 90s (before SRS) suffer this problem. It is common, and I have fixed many myself.
I was just under the dash of my '91 K2500 and scavenged a column from an '88 van. Your rig is similar.
Slight looseness "could" be the tilt-wheel wearing-out, as Rob says. This makes the truck very hard to control, Or if a very heavy-handed driver has been straining against the wheel, the plastic bushings may have been smooshed. If only slightly smooshed, no big deal; but if too-smooshed the thin part can buckle, fold-back, and wedge the shaft solid... very bad.
Where steering column meets plastic dash, there is a panel 10" wide. 2 screws in bottom, un-hook from top.
There is a V-shape bracket under the column. There are 4 screws run slant-ways through the V into the column. There are two screws straight up through the bracket ears into the dash framework.
Any of these could be loose. Or broken.
But you have to ask "why??" The factory puts them in pretty tight. They are very strong. Has the steering column been worked on? Most under-dash repairs can be done without taking the column out. Has the truck been in an accident? What ELSE is loose or broken? (An older truck can have a lot of un-seen broken bits.)
The 2 screws are part of a "break-away" system, the last stage in a front-end crash crumple. Their size, strength, tightness is critical for your safety.
RJ is right. If it is not clear to you WHY the column is loose, you should take it to an experienced mechanic. Any GM truck dealer should be qualified. Or ask snowplow or lawn-care contractors where they take their older work-trucks for repair.