Right, some confusion here as to what you are buying.
I have not seen one of these before, but as far as I can see, you are buying a twin set of LED lights, with control electronics, which can vary the power to the LEDs.
The power comes from a rechargeable battery, that can be charged over a long period of time. I will assume that this charger will not have enough power to drive the LED's directly. So using an inverter or DC power supply from 12 Volts will just not work the way you want it to.
Estimating the current required from the data given.
6400 mAh battery, yet the run time says <= 30 min.
So the units would consume 12.8 amps ( 6400 mA = 6.8 Amps so it will be double this if it only runs for half an hour) This MUST be wrong.:doh:doh
What you would need to do is remove the switch on the unit, as I guess you won't want to get out to press it every time you want to use it.
Remove the control electronics, and make up a regulated supply, with maybe a dropper resistor, maybe have both LED's in series, depending on the Vf ie forward voltage of the LED or voltage drop, which could be several volts, then choose a resistor to limit the current and a voltage stabiliser to cope with the range of voltage on the vehicle.
So not an easy task, unless you know what you are doing.
The data you have is incorrect, and I could have a better idea how to do this if more information was available on the LED.
I cannot believe that the current to the LED's will be this high, if it was tested in situe, ie when lit with the 8.4 volt battery, measure the current, and the voltage across the LED when lit, then I could advise you on how to build a circuit capable of delivering the required current, at the right voltage.
I certainly like the lights, and I can imagine a set on the front of my boat, but if they used 12 amps... forget it.
Hope this helps,
best regards,
Rustic