Hello Godzilla, first get a vom, Harbor Freight even sells them for as little as 3 bucks on sale.
Next measure battery voltage, this is a baseline. Then when you fire the engine you should be able to read the charging current.
If NOT then primary wiring is suspect, if so continue to what does not work.
Is the ground wire (black at battery box) clean and tight?
Yes you can fire the engine and read voltage at battery terminals to see alternator trying to charge the battery, IF the battery is VERY low, the Whizzer will not always charge it, in this case use trickle charger or motorcycle charger or "battery conditioner" if you have one. A trickle-charger can be made using a little black wall transformer that might power a walkman or something. Typically, if headlamp comes on with the key battery is in the range of the bike's abiliy to charge it.
If at anythime, you are not ready to externally charge the battery, unplug one headlight wire, and ride bike with headlight off to help charge battery.
You may be able to read the red wire (engine running wire off batt) for AC, if so regualtor should be suspect, light bulbs like AC batteries do not. Here you should also read charging voltage.
Do these things and report back with your findings and we can continue.
It would be hopeless for us to go thru the entire wiring loom if you have a bad ground or dirty connections.
Mike