Thanks for more useful links. You are right: I don't need the bulk and hassle of a battery and the KLX isn't fitted with one.
Currently, I am running lights on the stock single AC lighting coil which is now doing a much better job, since a 12V regulator has been fitted.
The next phases of the project could be:
1) Add a second winding to the AC coil, to deal with the brake light, without a battery.
2) Re-wire the AC coil onto a bridge rectifier, using DC/LED lights thereafter, without a battery. (with capacitors if required).
Regards
David