Speedometer Noise
Maybe I'm reading too much into it... but "graphite" in my mind is a fine powder, and "graphite oil" is liquid suspension of said powder.
So, "spraying graphite" into there is kinda unclear... kinda splitting hairs here but details like this can make all the difference in the world sometimes.
Disconnect the speedometer at the cluster. I think you may be able to remove the inner cable a few feet from the outer covering iirc. Clean off the really gnarly stuff. Lube the exposed cable thoroughly and squirt some more down inside the outside cover for good measure, we don't want to do this again. Reinstall cable. Go for a beer.
Maybe I'm reading too much into it... but "graphite" in my mind is a fine powder, and "graphite oil" is liquid suspension of said powder.
So, "spraying graphite" into there is kinda unclear... kinda splitting hairs here but details like this can make all the difference in the world sometimes.

But ya the solution Ford used from the factory was a graphite oil/super thin grease, There are different types of graphite lubricants from dry to oil to grease.
If you ever wonder why the lubricant on the cable is grey black, it is cause it is graphite it's not dirty, it's just full of graphite and that makes it look dirty.
The advantage of graphite as lubricant is it plates on to the surfaces creating a slippery barrier/coating. Even after the carrier drains out or evaporates off the graphite will remain to lubricant. Graphite lubricants are used in high temp applications up to 1000°F for this exact reason.
I personally have always recommended against greases in speedo cables.
The system has very low torque handling capabilities but it is able to be subjected to very high torque. Greases and the like can exert excessive torque on to the driven gear in the trans and the drive cable, this is even more likly if the vehicles sees sub zero temps, then these parts can wear prematurely I'v pulled a driven gear or 2 that the teeth were paper thin and folded over due to grease being used to lubricate the speedo cable.
Graphite oil is very thin and the oil acts more as a carrier than anything else and will not measurably thicken up in cold weather.
Speedo and tach cables are an application where graphite really is the most ideal lubricant to use.
Graphite Extreme lubricant | Jig-A-Loo
It sprays like anything else in a can, and is black as coal. It dries pretty quick.
I'm hoping to test drive today. It's not a big deal if it doesn't work. I'll pull the whole cable out if I have to. It appears to be in good condition (no rust or damage that I can see, and it's all tight).
Graphite spray on the cable itself, and I did dab a little clear grease on the square plastic end where it engages in the back of the speedo drive.












