With the engine off, no current is flowing in the starter circuit. So the voltage on the B+ connection of the starter (the thick wire) should be the same as the battery voltage. And the START connection of the starter (the thinner wire) should be close to zero volts. When you turn the key to “Start”, then the thin wire should be switched to something close to the battery voltage, but the battery voltage may be lower than 12.4 v at that point because of the current load the starter motor places on the battery. (If you disconnect the thin wire and just measure the voltage at the thin wire disconnected, then it should be nearly the same as the battery voltage with the key in “START”, but of course it won’t crank then. ) Like I mentioned, during cranking, the thick wire to the starter should measure above 10 or better 10.5 volts to insure good reliable cranking. If you don’t measure that, then there is a problem in either the battery, the connections, the ignition switch and any associated relays, or the wiring. (A shorted coil in the starter motor could cause this too.)
In practice it’s not so simple to measure these voltages during cranking. When I do it, I make up a set of long leads which I run from the starter motor into the passenger compartment, connected there to the meter, and I install some “T” adapters on the two starter terminals, so I can make a good connection by “T”-ing in using spade adapters to measure the voltages while I turn the key to START. I also put an adapter connected to the case of the starter motor for the ground connection to the meter.
Sounds like you are well on to a solution. Best of luck.