Hi,
If you use the on-board 12 V and sending for example 0.5 amps through the leds as a load, please keep in mind that you need a high wattage resistor, for example :
I count 24 led's in one circle, every led has a forward voltage of let's say 2 V, then you have 4 groups of 6 led's.
The total current would be 4 times the current in one leg, that means, let's say 4 times 0.5 amps is 2.0 amps DC current.
If you want the led's burn on, let's say, 0.2 A, then the total current in the system should be 0.8 A instead of 2.0 A. Per led that means a current drop of 0.3 A, if you look at a given voltage -current sheet, than for example you need to cut the voltage back from 2.0 to 1.4 per led. Doing so, that means a voltage drop of 12-(6*1.4)= 3.6 V
This 3.6 V voltage drop should be done by a resistor (R=3.6/0.8, R = 4.5 ohm) with a wattage of 3.6 * 0.8 = 2.88 Watt, and that's a lot of heat, especially in a closed environment.
A better idea is to put more led's in a string, but that's more difficult with a pre- assembled lamp.
jensen