Weird speedometer issues
There is a special speedometer cable lubricant.
What do you use to lubricate a noisy speedometer cable?
It should not get into the speedometer head itself, which takes a different lubricant. I can't remember what I used, but the needle is moved magnetically, it is not mechanically geared to the cable as the odometer is.
Edit: Just checked the factory manual. It says to remove the cable from the housing, and, after lubing the cable, wipe the top foot clean so it doesn't get into the speedometer head, as that can damage it.
Manual doesn't say anything about lubing the speedometer head (that I could find in a quick look), so I'm guessing Ma Mopar didn't anticipate we'd still be running these things 50-60 years later. Been a while since I lubed a speedo head (and they can get very noisy), but I think maybe I used 3-in-one oil. FWIW