I wonder if what you are measuring is
Galvanic Skin Response? It's a neat phenomena, which is most commonly utilised as part of polygraphs (so-called "lie detectors"). I considered doing this as a gimmicky sponsor wowing thing, but decided it would probably be against FIRST rules.
Off the top of my head it seems the easiest way to do this would be to build an
op-amp like this one and then connect it's output voltage to an appropriate transistor...
I'd love to hear the actual implementation details!