To confirm that you really do Not have a Mag switch problem ...
Unplug Both 6-Pin connectors that connect to the Trigger coils.
Make the following measurements on the connectors that connect to the Trigger Coils, NOT to the Ign Modules.
Place the Ignition Switches/Key in the OFF Position.
Using an Ohm Meter, Measure the BROWN Wires on each connector relative to Battery/Airframe Ground. Zero/Short is correct.
Place Ignition SwitchesKey in the BOTH Position. (Engine Stopped)
Again using an Ohm Meter, Measure the same BROWN Wires on each connector relative to Battery/Airframe Ground. O.L./Open is correct.
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Your symptoms do not support this wiring theory but it is worth trying.
It sound more like the Right module is coming alive after it gets some heat into it.
You can try dismounting the modules and after the Right one comes alive, cool it off and see if it dies.
An Ice Pack is cheap but messy.
A can of "Canned AIR / Dust Spray" will spray a super cold liquid (Freon) if you hold the can upside down.
This will chill the module quickly and evaporate completetly when finished.
Then you can be confident that the problem is the Module before spending $$$$$ on a module that you didn't need.
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Alternately you can swap all the connections from both modules and confirm that the Left side become the problem.
