AFAIK, there are two circuits here: the ignition/instrument/headlight (the one on the front) and the tail/brake/turn signal lights. I do not have my shop manual with me right now, but this is what I remember:
o The first/main circuit pretty much runs off the charger, but it could need the battery to complete it. It is very small (if I am not mistaken, it has coil, battery, headlight (high/low) switch, instrument pannel light, voltage regulator (in one way or another), key switch, and emergency stop switch). Everything else can pretty much be ignored.
o The battery could be needed to avoid making the voltage regulator rather annoyed
o The second circuit uses battery to operate; lights will be operational as soon as bike is in the "on" position
o Ignore for now the second circuit. It is nice to have but will not solve your problem
o To use the starter you need to hold one of the brake levers; that is not needed for the kickstart.
o FYI, I and my gf rode her 86 Spree (I am putting it together for her as a present) without the second circuit working at all: no brake lights or turn signals or even starter. It does not need any of them to run. Since I was given the scooter, I have been fixing it; now the only think left for me to repair in the electrical circuit is replace the switch on the left side (rear) brake lever.
o Did you check if the emergency stop switch is alive?
If you want, bug me and I will scan/mail you the schematics of both the entire scooter (I already scanned the 86 one) and the one just for the main circuit.