This could be capacitive coupling across the transformer and returning over the chassis to the 120v ground. Or if the neutral is broken in a way that allows it to capacitively couple with a ground wire, it could be a complete circuit through that coupling. Put a 24v load on the secondary (a pigtail socket with a 100w 120v light might do). If the former cause, the 12v may remain. If the latter cause, it should go away.
