Having already seen the insides of an Allen Bradley Type J potentiometer, I had noticed that there is a carbon type contact wiper inside (instead of the usual metal one), much like an electrical motor brush, with a rather large contact surface area. And it is rubbing against the thick electrically resistive carbon trace around the base of the pot. That's probably why it tends to cleans itself after several (many many actually) complete turns, back and forth from one end to the other.
True. Exercising a pot can help, but sometimes it doesn't always last.
Either way, in the case of the mod wheel pot, it should really be removed first if attempting it.
The normal shaft travel doesn't span the entire range of the pot.
When I rebuild such pots, I clean off the resistive tract and often replace the carbon wiper goody.
Some silver cement often helps.
But the resistive surface can get very glazed.
Only light abrasion (1500 grit or higher) can take it off.
Exercise can sometimes make things better, but with the original carbon wiper it can sometimes make things worse too.
It just reoccurs again.
Btw, I don't recommend abrading resistive elements unless absolutely necessary and then only on lower ohm pots.
Doing it on a 1 or 5 meg pot may ruin it.
Better to be king for a night than schmuck for a lifetime. - R. Pupkin