Hi,
Having moved from Central Michigan the beginning of Dec, to Daytona Beach, I've found that I now see more daylight even though we had the same time zone. I think it's because we are closer to the equator and actually see more sun than up north. Might be wrong and it's an illusion, but doesn't matter.
The answer is yes... run a light on a timer to come on around 4:00a and go off sometime after full sun, and again from almost getting dark to about 8:00p and you should see a remarkable change in laying patterns, provided food, water and other environmental elements remain unchanged (molting started or something).
We made that change and increased our egg production output... so you should get similar results.