Well if you turn the lights on and you get a problem then I would have to say it's electrical.
Check the voltage on the (+) wire on the coil with a voltmeter and see if the voltae drops when you turn the lights on. This is a good indication that your not getting enough power to the ignition system.
Voltage is just "Potential" it doesn't mean your getting full power when you need it.
I suspect that you should add a few grounds to the alternator and other places and check your connection on the positive side as well. Coroded power connections can lead to many problems. Grounds are usually overlooked so we harp on that quite a lot but poor connections on the positive side of the circuit can also lead to many electrical problems. MEasuring the voltage acroos the battery may not describe how the voltage is down the road. There are numerous terminal connections, crimps and switch contacts that can lead to poor performance.
You should check voltages while the engine is running also. THis prevents you from seeing faulse readings and prevents you from burning up your ICM and/or Coil.
Be super carefull with that fan when you start to run your test leads around the engine compartment. It takes a second to wrap your test leads around a fan hub. Don't ask...