Starter motor issue

I have a 1962 Lincoln Continental hardtop with a 430. It was running fine until a week ago. Suddenly, out of nowhere, when you turn on the ignition, there's a single click and nothing else. This click is coming from the external starter motor relay. I replaced the relay and I'm getting exactly the same thing. The battery is brand new and fully charged. When I turn the ignition switch, the voltage across the battery terminals drops to 12.05. So it can't be the battery. There's a 0.07 volt drop between the positive battery terminal and the post on the starter regardless of whether the ignition switch is turned or not. There's a 0.00 volt drop (so no drop at all) between the negative post of the battery and the starter motor housing when the ignition is off and a 0.03 volt drop when the ignition is engaged. So if my understanding is correct, there's no significant voltage drop. Is the starter motor broken?