Hairborn,
For Galvanic, one needs to have a complete electrical circuit. That circuit starts at the epilator, travels to the ground connection, which should have a wet sponge or something to assure good electrical connection. From there the electrons travel to where the probe is inserted, and then finally out the probe cable and back to the unit.
It should be pointed out that there are contra indicators to having glavanic electrolysis. Pregnant women should not use galvanic currents. Also, no metal should be between the ground and the probe. Example, I have steel pins in my right hip from a fracture that would not heal on its own. If I had a ground fastened to my right leg and was working anywhere on my upper body, then the electrons, seeking the path of least resistance would likely be attracted to the metal in the leg. So it is best to keep paths of electron flow clear of such possibilities.
Needless to say, things like pacemakers and diabetes should have a doctors approval.
As far as the foot switch is concerned, that does not make electrical connection to the body. It is only used to mechanically close the circuit and reopen it. I hope this helps to explain things a bit.