Welcome to the Benelli forum I have a 125 sport and like you say it is similar to the 2c.
the electronic ignition is feed directly from the flywheel and is separate from the lighting. I suggest that maybe someone has connected the ignition switch wrong as this is the only switch to have both circuits! The other problem might be a short circuit in the wiring loom bridging electric from the ignition system to the battery terminals.
i would be interested to see how you repaired the electronic ignition box? As the used to be unreliable!