If it is the cable binding, you will typically hear it making a chirping noise. If no noise is present, I'd inspect the gear on the end of the cable, and also ensure the gauge is functioning properly. I had a similar issue on a 91 years ago and it turned out to be the speedometer itself.
That is unfortunately sounding more and more like the speedometer. I'd take the cable loose and see if it spins, and look at the gear on the end first though before hunting for a speedometer just to make sure.