The problem here is that you are saying that because it looks like there are only lights on one side (from first person view in-game) that we should put lights only on one side of our armor...
Well, I know it looks like there are only lights on one side in game, but when you see the Master Chief from second person view, there are clearly lights on either side of the helmet. We aren't going to make the armor to reproduce a minor oversight in the first person view not matching the placement of the lights on the character model...
Have you considered that when you turn on the flashlight in the game, that it's most likely coming from the gun you are carrying???