You could use the 12 volts that operates the clutch on the cart to also operate a relay. This relay would make contact and be used in the place of the foot switch. This keeps the flexicoil switch and the 360 switch isolated from each other. the foot switch is a simple on-off switch - any toggle, relay or about any switch will work. Do not apply 12 volts directly to the 360 - use a relay for isolation.

john