It would be rare for a ballast resister to fail shorted or change resistance significantly but this could happen if the coils of the resister wire were twisted together which could cause a near short. The normal failure is an open which will allow the engine to start but it will die when the key is released to the run position.
To test, disconnect one wire from the resister and start the engine. If it continues to run when the key is released then you have 12 volts to the coil from the ignition switches' run position. That will burn the points again and/or cause the coil to fail if it is a 6 volt version.