My guess is the camera is just trying to adjust to the available lighting. It is probably on the threshold so it keeps flipping back and forth between light and dark. If it is only going by the light of the display, then it is really only going by the light bouncing off your face! So don't blink, smile, wiggle, or move forward or back in your seat as you will change the amount of light reflected.
Alternatively, put a small spot light on your face.