I believe it is the same LED for the light, only difference is the running light uses a resister to reduce the voltage on the LED and therefore make the LED's not as bright. I think there are three wires running back to the light (that is how my Nytro is) one is ground, and the other two are the hot leads for running and for brake. The resister is in the light itself. Have you had yours apart at all?
I would start by checking the wiring loom to the light and also checking the fuses. I don't know if the running and brake are on separate circuits.
You got a multimeter? Test the plug at the light. Once you find the ground, then one lead at the light should have a higher resistance than the other. If you get an open circuit reading, then the wires to the light are a problem. If it is good, then check the side going to the vehicle. I think both hot leads should give you 12 volts (the brake lead when the switch is activated).
I don't have an Apex and haven't seen the wiring diagram, let alone the light, so all of this could be BS and completely useless. Good Luck!