The light only comes on when the cubby door is opened. It's activated by the push button switch at the bottom of the door, which, when touched by a black plastic 'stalk', turns the light on.
It should come on whether the headlights are on or off.
The stalk on mine broke off so I've taken the bulb out. Need to find a way of sorting it out really.
It could be a break in the wiring somewhere as it's quite easy to damage the wires if someone removed the plastic surround in an over zealous manner.