The push-pull action of the shaft of the pot actuates a DPDT. You can use a lever or a slide or a rotator or whatever else you'd like to actuate a DPDT and get the same results by wiring it exactly per those directions.
It can also be accomplished via SPST, but you have to decide if you want to short or shunt.
It has been mentioned several times before that Hot Rails sound a bit weak when run in coil cut mode. I'd say you'd be better off attaching a series/parallel switch to the Hot Rails as opposed to a coil cut switch.