What is the largest distance you can place a contact closure away from a show controller? 24V?

Our guess is about 100 feet, although depending on the type of type of cable (shielded, twisted versus cat5, etc.), you might get away with 200-300 feet. Current draw is on the order of 15-20 mA, so line drop should not a big factor if you use 22Ga or larger wire. The environment is also a factor, where inductive devices like motors and contactors might persuade you to be more careful. With a 24 volt system however, you have a tremendous noise margin (maybe 12 volts) so induced noise is really not that big of an issue unless the turn on transition is slow, in which case you might get double triggering near the switch crossover point from the noisy line.