The resistance wire replaces the ballast resistor we used to see in older cars. It is actually used when the car is running not starting. The yellow wire that comes up from the starter supplies full battery voltage, via the thick purple start wire from the switch to the starter solenoid, to the coil for starting. Once the engine starts the resistance wire supplies a lower voltage for running. Only eight to nine volts is supplied to the coil to keep it from failing due to over heating. When the starter motor is engaged it draws a lot of power from the battery resulting in a lower voltage available to the coil. Full battery (reduced due to starter motor) voltage is supplied to the coil during starting as the voltage from the resistance wire would be reduced even more during starting, perhaps low enough to not fire the plugs enough to start. A higher voltage at the coil for the brief time it takes to start the engine isn't much of a threat to overheat the coil, but running the coil full time at alternator voltage of 14.8 volts is. Some coils have an internal resistance eliminating the need for a ballast resistor.

Sounds like a short to ground, perhaps it's insulation is worn and the wire is touching a part of the body and grounding. Or it could be as Doug suggests, the circuit grounding at the coil. I am also not familiar with the Mallory E start, but it sounds like an electronic ignition which would require 12 plus volts. If so and your ignition wire is already burn out you can replace it with a non insulated wire that will supply battery voltage to the coil. If it is a modification that converts points to a module type ignition you still may need the resistance wire. If so you will have to find a resistance wire to replace the burned out one, or use a regular wire and install a ballast resistor. The ignition system you have may require a specialized coil used for that system only, the blaster 2 may be the problem.

Did you install the E ignition yourself or did you buy the car with that already installed? Did the car run well before and this is just a problem that has recently come up?

Do you have the ignition wire attached to the pos + terminal of the coil? Do you have any other wires attached to the same pos + terminal that could be grounding?