The wire with 12 volts is power to the jack as well as power to the breakaway switch. The wire with continuity is most likely the trailer brake lead. To check this, simply apply 12 volts to the wire with continuity (make sure it has some kind of circuit protection in case we guessed wrong), and see if the brakes apply. The jack is self-grounding, and the breakaway switch doesn't use ground. The breakaway switch will operate with either wire connected to 12 volts.
Meddle not in the affairs of dragons, for you are crunchy, and taste good with ketchup.