That's how the resistor works. When current flows through, voltage drops and heat is created.
With the key in run and the points closed in the distributor, current flows through the ballast. On the run side its system voltage, on the other side its something less. 10.8 Volts is kindof low. Maybe the battery is low but maybe not. Next time you test that, go quickly measure the battery at the same time. A tenth or two is no big deal. A full volt between the battery (or alternator) and the run wires indicates poor connections.
Firewall connector or column connector? Regardless, clean them up and make sure the metal terminals inside aren't backing out.
