In order to get the speedo itself out of the housing, you'll have to carefully uncrimp the bezel and remove it, and then unscrew the two screws on the back of the housing. That will gain you access to the rest of the speedo, but there isn't much you can do.
I'd try putting some light oil in where the cable attaches (something like "3 in 1" oil - I have no idea whether your air tool oil would be appropriate.) Marvel Mystery Oil is probably the right viscosity, but don't know if their air tool oil is the same stuff.
[on edit] I think that graphite lock lube might be what you should use for the cable.
Last edited by klhansen; 01/02/2024 11:02 PM.