Hey Rickdb,
You might check to see if you have a "sweet spot" in the lever that controls the dump action.
On the '48 International KB5 I used to have, and on the '48 Chevy 2-ton I have now, with the PTO running, when I go to raise the bed, if I move the lever too fast, it will go past the "raise" position and nothing would happen. If I pull the lever back slowly, It will hit the "sweet spot" and the bed raises no problem. Pull it back some more and it slows down, pull it all the way back and it stops. Same thing on the way down...no problems. So in reality, it could use a stop at the bottom of the lever to keep it from moving farther forward than needed. You might look into that.
Also, that same lever in the cab is connected by linkage to the valve on the dump cylinder. Make sure that when you move the lever, you get coresponding movement in the linkage and the valve operation. If you move the lever and the valve doesn't move, then nothing is going to happen.
As far as vibration, yes...check the tires, most old truck tires die from deterioration before the tread runs out. Check the front wheel bearings and king pins as some of these old trucks seem to have the original sets still in them. Also check the drive line for bad u-joints and carrier bearing. If yours has the parking brake mounted on the transmission, check the drum to make sure it's all there and round.
And most important....SAFETY....When ever you raise the bed to work on the cylinder or anything under the bed that you cant get to underneath, Support the bed, I can't stress that enough. Use a couple sturdy 4x4 posts, one on each side of the frame, and prop them at an angle against the cross members of the bed. Make sure that what they're against is good and sound. You can also lay another 4x4 accross the frame back by the bed hinges and push it against the "V" of the frame and bed. Make sure that whatever you do, that bed doesn't come crashing down on you. I say this because A friend of mine lost his boss right in front of him when the bed of the dumptruck they were working on fell and crushed him, killing him instantly.
Sorry to hit a sad note but thats something to be aware of.
The big trucks are a blast to drive...I've had several and I'm hooked.....Good luck to you!
Rezman