Unless your timered light is on a dimmer also, and it gets dark at 4pm where you are, why not just set the timer to have light come on at 2am and go of after sunrise. They will still get 14 hours light, but they can see to go to bed by the setting sun, instead of stumbling around by being plunged into darkness with a light going off at 8.a few hours in the morning (beginning at 5am, I think), then off 9am-4pm as it is daylight, then on again 4-8pm. We only just installed this a week or so ago, so I can't speak to how much of an egg production impact it will have.
We were getting 7-9 eggs a day from 12 hens (although it seems our 3 white egg layers aren't even laying at all..or ever...so really 9 laying hens). As the natural light was reduced and we had not yet installed the artificial light, we had a decrease in egg production to around 3-5 per day. Now with the light on for the past week or so, we are around 4-6 eggs per day. We don't have production birds, so we would never expect a consistent 1/day from each hen anyway. If we get an avg of 5/day through the winter, I'll be happy.
Here is our electric set-up in the coop: The only reason we installed electric is because we had to completely re-do the electric in the barn due to chewed wires and old installation issues from previous owners. Otherwise, it would have been unlikely that we would have installed electric just for chickens. Also, this coop wall is about 24" (yes, 2 feet) behind the barn, so it was conveniently located.
View attachment 1584528