I had a casual friend who worked at Speedometer Repair Service here in ATL, and the way he explained it to me makes sense to my rednek head. The only linkage between the cable spin and the needle movement is magnetic, as explained above. As the magnet spins past the ferrous pole of the needle linkage, the magnet pulls on the pole piece, and deflects it in the clockwise direction. The faster the cable spins, the more hits per unit time the pole piece sees, and the further it gets tugged clockwise against the needle spring tension. There must be some damping in the spring movement to avoid flutter in the needle, either from needle linkage inertia or mechanical friction.

I've found the best way to lube a cable is with a light grease on the cable and use a drill on low speed to feed the cable into the housing, and inspect the cable closely for any kinks in the housing, and minimize the tightness of any bends where possible. I once replaced an a/t cable with one from an m/t truck, and it was a little shorter, and the resulting tighter bend at the firewall turnup wore out the replacement quickly.