Michael,
The cable comes out from the top (speedometer end). So try to remove it from the top. Sometimes they'll stick as a result of the expansion of the other end's wound wires in the transmission driven gear to which it fits. If so, they'll usually give in to a bit of twisting. If not, you'll have to remove the transmission great from under the car.

Regarding the little brass cup that holds the oil wick to the speedometer magnet shaft; it is best to replace it. Some speedometers have it at a 9 or 3 o'clock position which will allow oil to drip out. Of course, keeping dust out is also a good thing.

Having rebuilt or at minimum, cleaning, relubing and calibrating many of the Stewart Warner speedometers, the typical failure cause is drying of lube in either the main shaft (magnet shaft) or within the wheels of the odometer. This typically results in a larger and larger torque the cable has to drive. Then, the owner replaces the cable for it only to fail again in a few hundred miles.

If you are not going to clean the mechanism, then I suggest to give it an initial dose of penetrating oil and let it soak, then follow with a 20 weight, Clock Oil, Model Railroad Oil, or even 3 in 1. Marvel has sufficient viscosity, but I don't know if its film adherence is like that of the others.
Hope this helps,
PM

Hi Pat - thanks for the tip; I'll take a look at it over the weekend. I've had the car for 24 years and I've never once thought about lubing the cable. Time to take some action, I guess. As for the brass cup, will I see that when i'm under the dash taking off the cable housing? Mike.

Not sure. The cup is on the main frame of the speedometer and is typically inside the outer enclosure and require the removal of the front glass bezel then two screws release the inner frame from the rear enclosure. I'll take a look and send a photo if I can.
Pat

I squirted some garage door lube in the speedometer and it stop the noise