Hi Ramy!
The Schmidt Edelux headlight wires conventionally to the SON dynohub. It uses an internal AC-DC rectifier, so you do not have to observe lead/lug polarity when attaching the headlight to the SON dynohub, even though one of the wires is marked in white (the headlight sorts things out internally). Nothing special is required for wiring the headlight; two 4.8mm lugs on the wire to the two matching lugs on the dynohub.
The Supernova taillight is definitively DC only, and depends on the attachment to the headlight having the correct polarity. Here is the word on it from Peter White:
The Supernova E3 Pro headlight converts AC (alternating current) from the hub dynamo into DC (direct current) for the LEDs. The output from the E3 Pro headlight to the taillight (red & blue wires) is also DC. The taillight cannot use the AC from the hub dynamo, it must receive only DC. The electronics that convert AC to DC are only in the headlight, not in the taillight. So, you must never attach the 161-T taillight directly to a dynamo. It can only be used when attached to the red & blue output wires from the E3 Pro headlight, or the E3 Triple.
per
http://www.peterwhitecycles.com/supernova.asp The Edelux headlight uses 2.8mm metric connectors for the taillight, and they are polarized, thanks to the headlight's internal rectifier. The headlight has a standlight, and the headlight powers the taillight, however, Schmidt recommend connecting a diode rear light with its own stand light. I believe they are saying the headlight's built-in standlight capacitor lacks capacity for double standlight operation. This is essentially the same as, say a B&M IQ Cyo-series headlight with standlight (same basic internals as the Edelux), which also requires the taillight have standlight capacity of its own. When used with the
Supernova E3 front light, I have confirmed the taillight has standlight capability.
As for running an LED taillight, Schmidt say...
Important when connecting the rear light transmission to the E delux:
a) the rear light terminal of the E delux must match the phase connection (usually with a bolt in to be connected) of the rear light - not with the ground connection.
So, yes, you do have to observe correct polarity when wiring the Supernova taillight to the Schmidt headlight. Get it wrong and it won't work. Reverse the connections and all should be fine.
Hope this helps. To recap: Edelux headlight wire to dynamo polarity doesn't matter. LED Supernova taillight to Edelux headlight requires correct polarity. Get it wrong, won't work but no damage; reverse and all will be well.
Be sure to insulate the spade connector that connects the taillight wire to the Edelux or it can short against the headlight's aluminum body. Julian's (as shown in his photo above) is a very nicely done example, complete with offset connections so polarity is observed automatically when re-connecting.
Best,
Dan.