If the interrupter, whether mechanical or electronical, is suddenly opening, without this capacitor an enormous inductive kick voltage would develop. This would be deadly to the mechanical interrupter, because it would totally burn-down. Here the capacitor is needed to keep it alive.
With the transistorized ignition system, this capacitor is also needed, although there exists an additonal zener protection: In order to achieve a stable ignition voltage (35kV), which is created by the principle of induction, the duration of collapse of magnetic field must be very well controlled. The capacitance and inductance of primary winding of ignition coil form a characteristic time constant in order to produce a stable and well formed spark.



Imagine, that no capacitor was connected across interrupter. Then, rise time of potential change on this cable (between interrupter output and ignition coil) would be very high. This would cause the emission of extreme interference.



Hmm. I don't think that this capacitor should be an electrolytic one. Electrolytics are highly unstable, especially at the high temperatures, that typically exist near the motor! More, they show a huge change of performance when temperature changes.
Also, typical transistor of a transistorized ignition system is protected by a zener barrier of about 320V and can withstand a collector emitter voltage of about 400V. So, nominal voltage of this capacitor should also be at least 400V.
I would use a polypropylen foil capacitor rated at 630V for this task. By the way, my car doesn't have this capacitor. It's already built-in, in the ignition modul.

Kai