Is this an export thing? The footswitches I've seen on this side of the pond use Heyco strain relief bushings where the cable enters the pedal.
At the typical Fender 2-button footswitch you need:
Ground - provided by the reverb cable's shield, common to both switches.
Reverb switch return - the signal wire in the shielded cable.
Vibrato switch return - the separate (white) wire inside the cable jacket.
A stereo jack and plug should work. Might make funny, loud noises if it's ever plugged or unplugged while the amp is on...