Speedometer not working but odometer works fine on my 1959 Cadillac. I have already tried lube on cable wire.
If the odometer works but the speedometer doesn’t, it means the gauge itself has gone bad. It’s time to replace the speedometer. Sorry, no other explanation. The speedometer on this vehicle and the odometer are tied together. The cable is not the problem as the odometer is working, the problem is also not in the worm gear in the transmission.
You may be able to fix this yourself easily enough. Remove the speedometer and note the gears on the axles. If one gear spins freely when it should turn with the axle, a drop of superglue will fix the instrument. Give it a try.
The speedometer on vehicles of this vintage usually consist of a permanent magnet spinning inside a steel cup. The needle is attached to the cup, that faster the magnet spins, the more the cup moves.
The odometer is also driven by the cable through a gear reduction. Chances are that the magnet broke off.