There are 3 reasons we experience eye fatigue when staring at a screen in a dark room:
1. Overloading your cones with a bright, concentrated light source (your TV or monitor).
2. Under-saturating your rods from a lack of ambient lighting.
3. Frequent pupil dilation from the extreme light changes on the screen.
When you look directly at a screen in a dark room your eyes will dilate which causes your cones to overload with bright color and detail. Meanwhile, your rods are working hard to make sense of your surroundings in the darkness all around you, but don't have enough light to work properly. This is because when there is no ambient light in the room, your rods have no light to work with.
On top of this, since the main source of light in the room is the screen, which constantly changes from bright to dark, your eyes are constantly dilating big-small-big-small-big-small...
When your eyes’ cones and rods are able to work together, fatigue is much less likely. The best way to relieve eye strain while watching TV is to leave the lights on, but let’s get real: most of us would rather die than watch TV with screen-glare from the lights on.