A basic test lamp wont be adequate in this case. There is enough current to enegize and run the starter. We know that much. We dont know we have adequate voltage on the brown ign.2 or blue ign.1 without a volt meter.
Just the addition of an electric choke can rob the voltage needed if the voltage was already border line low.
I would replace an ignition switch that is already known bad, then see if another problem exists.