I posted photos of my brooder in the coop under a droppings board above. I only have one regular-sized window in my 8' x 12', that window is on the north side of the coop and I'm north of the equator. I have a red heat lamp when I'm brooding young chicks but no light when I'm using it as a broody buster or isolating a chicken that needs isolating. With four windows in your coop I have trouble imagining it being all that dark under there but you are looking at it, I'm not.
If you decide you do need to add light, I'd agree with a small LED on a timer for daylight only. You don't want to disturb the other chickens' sleep. A light at night could mess with their egg laying.
If you decide you do need to add light, I'd agree with a small LED on a timer for daylight only. You don't want to disturb the other chickens' sleep. A light at night could mess with their egg laying.