Hi Ted,
OK, I've had a rummage in the shed (what a job), and this is what I've found out.
I'm sorry if this is long winded, but I've tried to explain everything you asked for, and I hope it helps.
Firstly, this is the amount of stuff I had to shift to find my scooter box....

It's in here somewhere...

Nearly There...

The (green) scooter bits box...
Right, Here goes. The head unit I have looks like this....

and this is the reverse side....

I have drawn out the wiring and scanned it into the computer, I just hope that you can see it OK....

But if you can't, just send me a P.M, with an address (or an e-mail), and I'll post it to you.
In this shot, You can see the switches. The 'Power On / Ignition switch is on the left side (phono connector), with the Headlamp switch on the Bottom right (yellow in-line fuse unit attached).
The 'Pot' at the top of the picture is the 'Wig-Wag' Forward / Reverse control. This has Red, Yellow, and Orange wires attached to it.

The Speed 'Pot' is set into the plastic case (top left of unit), and has three terminals which are pointing to the
left as you look at the BOTTOM of the pot. They all start off Black, but they then connect (via small spade connectors) as follows....
The one on the bottom of the 'Pot' connects to a
Red / Yellow wire, which goes to
pin 13 on the White '
Multipin' connection in the top Right of the board....

The one in the Center, connects to a
Yellow wire, which goes to the
Center terminal on the 'Wig-Wag' pot. and the one at the top, connects to a
Green wire, which goes to
pin 5 on the White connector.
The 'Wig-Wag' pot is loose, as this mounts lower in the casing. If you set the three terminals to point
Right (as viewed from below), the wires are as follows...
The Bottom one is Orange, and goes to
pin 3 on the White connector, the Center one (Yellow) goes to the Speed pot, and the top wire is Red and goes to
pin 2 on the White connector.
I hope that this is easy to follow, and is helping you make sense of everything.
On the wiring diagram, I have also drawn the wiring for the Headlight switch, the Power On / Ignition switch, the Battery Meter, and the Horn Push / Buzzer.
There are two wires which don't seem to connect anywhere, and these are a Purple from pin 7, and a Grey from pin 8.
There is also a
Red multipin connector, which connects to the Head unit Board....

this goes to the Control Unit....

and plugs into the White, 9 pin connector on the right of the picture.
This is a shot of the control Unit, the top side....

and the internals....

But I haven't removed any wires from the inside of this, just from the multiple plugs on it's outside.
And finally the charger....

Which lived permanently in the 'Boot' of the scooter, and connects to a 3 pin plug on the controller.
Keep Busy,
Regards,
Mark.