So, if you spin the cable manually, it all acts smoothly and like it should, the needle returning to "0" when the turning stops?
The cable indexes with ONE speed cup, the one that's attached to it mechanically. That speed cup has the bar magnet in it, which the cable revolutions spin in direct proportion to transmission output shaft speed.
That speed cup fits just inside of another speed cup, the one that has the needle attached to it. They have very little clearance between them, so that any wear of the bushings can allow them to touch (with appropriate mechanical scraping noises!).
As the speed cup with the bar magnet turns, the magnetism wants to make the second speed cup follow it in rotational speed. The level of basic magnetism is how you adjust the speed, when that part of the speedometer is calibrated when it's new. So as the cable-attached speed cup spins, the needle-attached speed cup seeks to match it, but the small clockspring attached to the needle size is a resistance to that and makes sure the needle returns to "0" or lower speeds as the vehicle speed slows or stops.
The odometer is the ONLY other thing that's cable-driven, via a few gears, as the speedometer cable turns.
The basic distance calibration, which will relate to the speed calibration, are the two gears which are in the transmission tailshaft housing. One retained to the output shaft by a clip (drive gear) and the other gear which is a part of the "adapter", what the cable housing attaches to on the transmission tailshaft housing. The lower part of the cable slides into the shaft on that gear in a positive manner.
Those lower gears can be metal or plastic, not sure for your particular vehicle, AND they can wear with use over time. Just as the shaft of the driven gear and the adapter can also wear. All use "splash" transmission fluid for lubrication. The output of their gear teeth combination (ratio) results in a specific range of "revolutions/mile" for that gear set and the speedometer cable.
On some vehicles, when an existing speedo gear combination might not be accurate enough for a given rear axle ratio and tire size, then a "ratio adapter" can be added at the transmission end. The ratio inside of the adapter will be stamped on its outer case surface.
For the sake of "Theory of Operation", we'll not worry about anything at the bottom side of things other than possible wear issues of the moving parts down there. The gear ratio down there is another situation, itself, which relates to the number of times the speedometer cable turns as the vehicle travels over a one mile distance (revs/mile).
So the speedometer cable turns as it comes out of the transmission. The cable mechanically indexes with the slot in the back of the speedometer head. The rear part of the speed cup with the bar magnet in it. The odometer runs off of this part of things, via gears.
As the back speed cup turns, the magnetism level makes the front side of the other speed cup turn, too. The level of magnetism in the bar magnet can be varied by what I term "a zapper gun" which the speedometer shops use to do the indicated speed calibration of the speedometer unit. A trial/error method at best, from what I've seen.
The small clockspring modulates how the speedometer needle acts, usually, making sure it returns to its resting position, or a lower indicated speed, as the vehicle slows down. This all might be a little bit redundant from what I mentioned above, but I wanted to lay out the progression of things, just to make sure.
The observed normal wear item in the speedometer head is the rear speed cup bearing/bushing. Which could be a bronze bushing or a plastic one, depending upon model year, from the factory. The speedometer shops usually put in a bronze bushing in modern speedometer heads. This is a possibly more accurate way to also keep the two speed cups from touching as they spin, too.
On the cable side of things, this is a wear point also! Which is where the lube comes in. There is a specific speedometer lube. The ACDelco lube is kind of like Dippity-Do hair gel from the '60s. A kind of "springy" gel, with lubricating properties (which Dippity-Do didn't have). Powdered graphite (or lubes with powdered graphite in them) was also used in prior times, when all of the casings were flexible metal casings.
Wear in the casing can lead to wavering speed readings, at lower speeds. As can a cable that gets worn and "kinks" itself. As the cable is laid on a work bench, slowly rolled at one end, it should roll uniformly from end to end, with no visible "kinks" in the works.
If the speedometer casing and shaft have accumulated wear in them, a type of sympathetic resonance can happen which will cause the needle to waver rather than be "rock solid" at a constant vehicle speed. The only option is replacement of the casing and the shaft within. Probably best to get these from a reputable speedometer restoration facility than a "cut/fit/" situation form an auto supply, I believe. But that's just me.
Does your speedometer head have a screw-on cap for the cable unit or does it snap on with a retainer? Reason I ask is if it's a "cap", you might back off the tightening a thread or so, so see if the cable is being forced too far into the speedometer's rear speed cup. Purely as a possible diagnostic situation. Make sure it's still firmly attached to the housing, though.
The whole operation of the unit might not be nearly as "involved" as my description, once you see how it operates. Keep us posted on your progress.
Happy NEW YEAR!
CBODY67