68 barracuda speedometer issue

Speedometer issues often appear when the climate changes to very cold. Clean and lube cable/sheathe could cure it.
To poke more grease in that square drive hole at back of the instrument without cleaning what is in there out good first can do the instrument more harm that good.
On the other hand, if climate change can be ruled out and If the cable has been applying pressure to that input to the point that parts inside the speedometer are now colliding... The damage is done. Instrument service will be needed. Good luck with it.