It may just be dry and the actual cable is binding on the ID of the sheathing. So, instead of a smooth rotation it catches and releases over and over - and you get a jumpy inaccurate reading at the dash. Often a thorough flush and lube job will get another 20 years out of it.
To do this properly, you will need to disconnect the cable/sheathing at both ends.
To disco the drive end is fairly straight forward. Just follow the cable from the firewall to where it is attached to the transfer case/transmission. There should be a round fitting at the end that threads on to coupling on the transmission/TC housing. Unscrew it and pull the cable from the drive gear.
On the other end - where it connects to the speedometer head - the sheathing terminates with a bell shaped coupling. The coupling has a raised lip on the outer edge that is captured by a spring clip on the back of the instrument panel. Download the image below and zoom in on the yellow circle - you'll see the clip:
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Reach up under the dash and locate the cable to speedometer head interface. The clip is on the top of the coupling. While applying gentle tension on the cable, push the clip up and towards the cluster. The coupling should pop free and the cable should disengage from the speedometer head.
With both ends of the cable open, you can flush any debris, dried up lubricant, etc out. This is done from the top (dash) end down to the bottom (transmission) end. Normally this is done by pulling the instrument cluster out of the dash and working from inside the cab.
But, since you are not familiar with these trucks, you might not feel like learning the cluster removal procedure ( and I don't feel like writing it tonight). Consider this:
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The image above shows where and how the speedometer cable penetrates the firewall. Use a screwdriver, putty knife, or whatever to pop the gland free from the opening in the wall. The draw the speedometer cable into the engine compartment. With the open end of the sheathing in the engine comp, you can point it straight up and dump your choice of solvent down into the ID of the sheathing. You can use gasoline, acetone, MEK, degreaser, PBlaster, brakekleen, carb cleaner... whatever you have on hand.
But what ever you use, the key to this job is to be constantly spinning the cable within the sheathing while the solvent is flowing down and out the transmission end. You might want to catch the solvent in a pan as it flows out the bottom. It will be a lot dirtier when it exits at the bottom end than it was when it went in the top.
When you feel the cable and sheathing ID have been flushed - and the cable spins freely with your fingertips - start lubricating. Actually, I think the preferred lube is dry powdered graphite. Just like they sell to spray into your door locks. The fact that it is dry keeps it in the sheathing - and not able to migrate up into the speedometer head where it could cause problems.
After it is cleaned, flushed and lubed - the speedometer cable can be re-coupled at both ends.
