Still need to know if it's just one coil or both. If it's one I have an idea.

if it were a multi cylinder engine No 1 spark plug would fire on compression and maybe No 3 on exhaust, as we have 2 cylinders the coil fires through one plug then the next plug, we would need 2 coils to fire one cylinder otherwise, lots of hardly dangerous owners take the one coil off which throws a spark through each plug : they only have 1 per cylinder so it goes through one on compression and the other on exhaust and replace that with 2 coils thinking they will go faster or at least make more noise, if 1 coil is burning out as in hot as or smoking it could be that the ign module is allowing the primary voltage / current to flow for to long thus overheating the coil, with modern ignition systems the " dwell " as its called is controlled by the ign module that is the time allowed to build up the magnetic field in the primary side of the coil and the higher the revs the more time it gets, when the key is on and the motor not running the ign module will stop current flowing to ground through the module, if it didn't the coil would overheat very quickly because of the high current used by the coil, now I am confused

Years ago a ballast resistor was used to reduce the voltage to the coil while the engine was running. That kept the coil from overheating. During starting full voltage was allowed to the coil to compensate for the reduced battery voltage while cranking.

What I'm wondering is if the same reduced current/voltage can be accomplished electronically on the ground side and if the igniter somehow reduces the voltage from the ground side while the engine is running. a problem with that circuit could possibly overheat the coil. Maybe there's an electronics engineer here that would know if that could be done.

I think if the dwell was too long that cylinder probably wouldn't fire at all. I can still remember adjusting the dwell on the old distributors and you could tell if it wasn't right.

The answer to your question No, what happens is without the motor turning over the ign module stops the current flow through the coil, then as the motor is cranked over the module picks this up and allows current to flow for a given time for that rpm, its a very short time that is needed to create a magnetic field in the primary circuit. the current draw of a modern coil is lots more than a system with points and a resistor, you are correct in that resistor was there to reduce the heat build up in the coil and the side benefit was to allow a strong spark when starting