On Motoplat systems that second wire suppllies the horn and tail/stop light while the 'normal' lighting coil is for the headlight. Basically two lighting coils with a common earth. You can not parrallel the lighting coils (ie connect the two supplies together because they are actually AC supplies and out of phase because of the different mounting position of the coil within the flywheel.
Naturally the output of the lighting system is that small that at idle you can not even see the lights working or hear the horn
You have to rev the engine quite high to get the system to work and even then you need a torch to see if the headlight is on
You can not run a battery at the same time as using the lighting coils without designing a rectifier system and regulator otherwise you wil fry something. The battery is pure DC while the lighting coil output is very crude AC.
If it is a Motoplat you just have to learn to live with it and eat plenty of carrots
Not sure about other systems but believe Femsa and SEM are similiar.