the reason I ask about the external resistor has to do with your symptom of shutting off after starting, which may mean the coil itself (not the resistor) is not getting power when the key is allowed to return to in the "run" position. if the resistor or related wiring is bad, this can happen.
First thing is a good tuneup and dry inside the distributor cap, then have you tried to jump a wire from battery positive to the + side of the coil and see if it runs then?
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