95 Sidekick Gear shifter light, does it light up with headlights?

When you turn on your headlight, are the gearshifter selector lights supposed to light up?

mine didn't , never looked to see if there was a bulb

On my Sidekick, when I take out my ashtray there is a little green bulb that comes on with the headlights, but it is not connected to anything and has a fairly short wire on it, do you think this light can be connected to the gearshifter, or does that light hook up somewhere else that I should know about?

i found the same light when i was putting a new CD player in , couldnt find where it went so i just unhooked it