If I remember reading about them, the Runtz is a 3 terminal regulator, not a resistor. That means that the 12 v feed comes in one lead, there must be a ground connected and the output will be your 6 v. I would expect the 6v to appear correctly without any load attached. Your battery charger will not give you a correct 6v for testing, with no load. It will produce peaked sinusoid half wave forms that are much higher than 6 v.
