G'day matesrates.
To determine if the white wire is suitable for your purpose, you need to work out how much current the lights consume. It seems that no more than 3W can be drawn from the white wire and that even then it affects engine performance.
My guess is that your lights will consume too much power.
Do you have a multimeter?
To use the white wire, you'll also need a rectifier diode to convert from AC to DC, then at least a 3W Zener diode, (~4.7V or 5.1V for 3 x batteries), as a shunt to regulate the voltage, or else a series current-limiting resistor for a trickle charge. (Not suitable for continuous light usage.)
I'm in the midst of fitting a 100W generator to mine, with an 18W/18W x 2 dual headlight, capable of going 18W-36W-54W-72W, powered by a 12V 5Ah SLA battery mounted under the tank. (I'll normally use 18W as 'low' and 36W as 'high'.)
Sing out if I can help more.
I also regularly get cars coming at me through 'STOP' signs, thinking I'm doing 20kph and not 40kph, hence the extra-bright lighting.
On an aside, which part of Sydney are you from? I'm in Nowra.