Weird speedometer problem

Weird....I agree. The speedometer system on these cars are not too complicated...and your on the right track to your solution....but you need to consider the variables for your symptom.

The Speedocable is driven off the output shaft of the transmission, with a speedometer output gear that is Plastic....and the variable here is the WEAR, unless its brand new..

The Cable is then inserted in the end, and is driven through the Speedo Cable Housing till the Square End plugs into the actual Speedometer.

If the cable spins freely by your fingers inserted in 90% of the cable housing.....not all the way up to the cluster all the way.....you can assume your housing is ok.....

I think your output gear is worn.....or not properly engaged/clocked on the output shaft.

Best way to grease the Speedo Cable Housing is with a Grease gun....

My speedo squeeks when its below 40* outside.....otherwise its pretty steady and does not bounce alot...(not to say it doesnt bounce a little)

With more information......we can deduce your concern....No Problem.