66 Valiant Electrical Issue?

Does everything have to be hooked up in order to function? Like does the headlight switch have to be plugged in in order for the wipers to work and so forth??

I unplugged the power wire (black) coming from the alternator and there isn't enough power coming through the burnt splice to light the bulb but there's enough to arc out on if grounded.
Could it be the alternator? What about the voltage regulator?