correct, the resistor is to cut down the 12V to coil, so the 10V reading is fine, not starting hot probably has nothing to do with that voltage to the coil, BUT there should be a circuit that bypasses the resistor when the starter is engaged so it gets the full 12V then, ensuring a good spark when the starter load is high, maybe that circuit is missing .... how is it acting when it won't start? won't crank? cranks slow? won't fire?
Bill