Richard,
The standard ignition module powers down to prevent the coil cooking if it doesn't see a pulse from the hall effect sensor (bean can). I did put a scope on one a couple of years ago but cannot remember how quickly it goes down but it's less than a second. The kickstart module keeps the power on the coil for a longer period of time to give you chance to kick it over.
There's no intelligence in the trigger unit it simply looks for a logic 0 from the hall sensor and fires the coil, the advance/retard is all handled by the mechanical unit in the bean can. when the engine turns for the first time the first pulse from the hall sensor "wakes" the trigger unit up and it powers up the coil. The second pulse causes the trigger to fire normally if it doesn't see a pulse within a fraction of a second it simply shuts down the power to the coil. Obviously while your fumbling with the awkward slow kickstart all you are doing is waking the unit up and it's shutting down again because you are not turning the engine over fast enough.
If you put a multimeter on the output to the coil you'll see how quickly it powers down.
