Sorry I hadn't gotten back to this thread earlier.
Going back to the OP, I think that if you have the lights come on in the morning, but the door is closed and there is no food and water for the chickens, then they would be more agitated. They will naturally be hungry and wanting food when they wake up.
If you can't rat proof the coop, to allow the chickens food and water in there, then you might want to go without the added lighting.
The other choice would be to extend the day, in the evening, when they have a full crop. You could also leave some food out for them at night. Just enough to keep them busy for a little while, but not enough to leave any leftovers for rodents. Maybe a little treat of scratch.
Our coop has windows. The chickens settle down and go to roost, even when they have a light on in the evenings. I think it's because it gets darker in the coop, as the sun goes down, even though it isn't totally dark. They can still tell a difference. Dimmer lighting would help you with this.
As a parrot owner, I'm familiar with 12 hour days. It's important for parrots to get adequate sleep.
I like having some light on in the coop in the evenings. I like to be able to see on the web cam, that the automatic door closed and that all the chickens are inside. In the most frigid of winters, I like the chickens to be able to eat a little later into the evening, on the shortest and coldest of days. In other years, when I was working full time in the city, it gave me time to get home and do what I needed to do in the coop, without shocking and startling the chickens, turning on the lights. I'm mentioning this, since others have questioned why anyone would have light in the coop.