Don't go any smaller than 16 guage. 14 would be better. But, most auto parts stores sell three-wire accessory wire, which is a roll of three wires joined next to each other, but in a different color insulation (think speaker wire, but with three wires instead of two). It's used alot for wiring trailers. if you live near an RV dealer, they would have it to. Something like that would be a much better choice than stringing several single wires together. Neater, too.
Take care,
-Chris
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