I'm driving along and hear a tick tick tick tick coming from what appears to be my dashboard. I put the car in neutral and the engine RPM is drop and the ticking remains at speed, so I"m guessing that it is the speedometer cable and not something in the engine.
The ticking speeds up and slows down with the speed of the car and not with the speed of the engine.

 

Year? Auto? Manual?

 

Simple, really. Reach under the dash to find the clip on back of speedo that retains the cable; squeeze the clip and pull it out and drag that end of the cable down and below the lip of the dash pad. Get a shop rag and hold it in one hand with the end of the cable; with the other hand, grab the plastic (or metal) square-drive end of the cable and start pulling it out of the sheath while wiping the grease/graphite/? off with the shop rag. Graphite is black and nasty stuff to get off of carpets, etc....so you NEED the shop rag to get excess off as it comes out of the cable sheath.

Look for any areas of rubbing, unwinding of cable wires, damage. If you see rubbing but no damage on the cable, the inside of the sheath is failing and you need a whole new cable. If cable is dry or unlubed, buy a squeeze tube of dry graphite lubricant. To apply it, squeeze some into a clean shop towel/rag, then drag the cable back thru that patch of graphite as you stuff the cable back in the sheath. You don't need a lot...you just want a wipe on the whole cable. DO NOT use oil as it will wick up the cable as it spins and put oil inside the speedo housing . When the cable is all the way in, rotate the square-drive end while pushing it in farther, as the other end has to engage its drive end with the speedo drive gear. When seated, push the cable end back up to the speedo, squeeze the retaining clip, and insert the end into the speedo drive hub. Release clip....you're done.

If you have to replace the whole cable, you will need to get under the car with a 7/16" open-end wrench, loosen the retainer bolt on the transmission, move retainer out of the way or remove it, pull the cable out of the drive gear. Now you have to fish the speedo end out of the firewall. There will be some dum-dum (black gummy sealer) involved at the thru hole (or maybe only a grommet to remove). Reverse the process to install the new cable.

 

If you have the big rubber bushing / grommet thats the heardest part, putting it back in the fire wall. I used vaseline / silicone jelly. Its the easiest way, otherwise its like trying to do a root canal in the bathroom mirror

 

'81 auto trans

 

be careful not to loose the drive gear off of the end of the cable into the trans

 

Had the identical clicking issue last Summer. The cable nub at the speedo wears down and can't grab the speedo. I tried nursing the original cable with lube, but it will slip out again and cause the same clicking. The prevailing new speedo cable sold by our C3 suppliers was affordable and surprisingly much superior to the original cable - including being smooth as silk (remember to lube it per "7T1") and an inch or two longer so you can more easily guide it back into it's speedo seat. Assuming you have cruise control, order the "upper" cable (and, specify cruise version). In short, it is quite simple to replace if (only if) you are limber enough to reach up behind the cluster and depress the speedo's affixment spring clip with, say, your index finger. Google its image to see what it looks like/operates.
Then, unscrew the other end - it is the upper cable attached to the cruise control transducer. Then, just unseat the firewall grommet and pull out the cable from under the hood.
Reach back up under the dash to click-seat the new cable, screw the other end back into the transducer, and reseat & reseal (silicone) the cable- firewall grommet that keeps out water, noise and smells. A satisfying and surprisingly easy and likely a lpermanent fix to an annoying problem.

Good luck -