It's just a resistor. They develop poor electric connections and stop working. Your mode of failure is slightly unusual. Often they'll work fine when cold, but cause cutting out when the car gets hot. Let it cool a bit and it'll work fine again.
All it's doing is dropping the voltage at the coil when the car is running to 8 volts or so. When the car is starting the coil gets a full 12 volts and delivers a bigger spark. It'll work at 12 volts, but it'll get hot when run full time like that. Any old ballast resistor will do the job. But I reckon a new 12 volt coil is a more elegant solution.
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