Usually, its just a matter of the cable breaking or being stripped.

Nice to see your car on the front page of the current issue of Old Autos
Keep on Cruising!!!
Dave

I just ran into speedo problems myself.

Removed 6cyl Buick and 3spd auto trans from a good running car (been driving it for years, speedo has always worked). Installed a 350 and 3spd auto trans. The two transmissions were different where the speedo gear is installed so I couldn't just move the speedo "bullet" and driven gear from one trans to the next so I dug through my pile of crap and found a bullet that will work and a driven gear.

Got the car running/driving and was hearing a clunking from the trans and watched the speedo needle jump in time with the clunks. Figured the noise was speedo related. I know the speedometer itself works fine and is quiet. I know the cable I am reusing works fine and is quiet so it has to do with the bullet/driven gear.

I got under the car today, pulled the bullet, swapped in a different coloured driven gear and ... noise gone (no idea whether the speedo is accurate but at least the noise is gone so I can now research what colour gears I need to install for the speedo to be accurate.

Here is why I mentioned this ...

I understand this car is new to you. Have you driven it and did the speedo work (quietly and smoothly) at some point during your ownership or did you purchase this car with a dead speedo? The reason I ask is this: When I installed the wrong driven gear (by wrong I mean that even though it was a TH350 driven gear I don't think it was designed to work with the drive gear in the trans) I am sure that in short order it would have been stripped. If you bought the car with the speedo not working, it could be that the stripped gear you removed from the trans is simply not compatible with the driven gear and you replaced the stripped gear with the same colour ... ending up with the same issue of driven and drive gears not compatible, ending up with a stripped gear once again. Not suggesting this IS your problem, just saying it could be ... the speedo itself could also have locked up, stopping the cable, stopping the driven gear, causing it to strip.

Good luck and keep us posted.

Take the head apart and lube it. Its is probably dried out.

I agree with RWW it probably needs lubed you need to pull to replace it.the work is the same so before buying an other one with possibly same problem.use a light oil like 3 in 1 put a couple of drops in the hole where cable would go you will probably see the bronze? bushing I would use a green handled robertson screw driver to try and turn go easy but firmly.using a drill will only result in an other broken cable if not even a broken head.

You could post a pic of the stripped gear, someone might have one laying around. What transmission?