need help with a switch

thanks AJ, it looks like the pump has silly noids on them, so we are talking about relatively low draws

here is a wiring diagram for the remote i have now


it all makes sense to me, except for the white "common" wire
i dont know what that one does

if i see this correctly, i can draw from the black wire to light my switch
i should be capable of running a dedicated ground for it, thats no issue

but i guess im at a loss for what the point of the white wire is

(in my mind, i simply needed to close the circuit between black and green to lower it, and red and white to raise it, but that just dont make no sense now)