I would try to darken the lens, but not with a marker. First, tape a lens from an old pair of sunglasses over it and then observe to see if it closes early enough, or if it can be then adjusted to be right. If you do not have an old or broken pair of sunglasses, then tape your good pair to where one of the lenses is over the electric eye. A timer would be a constant pain.
We go out at dusk and close our two guillotine-type pop-doors, even tho our pen is 6'tall, steel fence set in cement, with four courses of hot wire running around it. You never know when you might have a power failure in the middle of the night.