Glad you asked the question and I would like to offer some advice.. (free of course

).
Here are some facts that can be verified if you search out the information.
Solar lighting usually is very weak, so the light source is usually LED.
The factor for chickens to be fooled into laying more eggs occurs in their brain. The light spectrum that does the brain stimulus is absent in the LED light spectrum. (I have read on this subject here on BYC that was posted by some well educated veterinary/poultry experts. I can find their postings but it would take me a little time to find).
So with the induced light not being really very beneficial here are my suggestions.
Get a battery powered light and install into coop. (light will run long since LED do not consume much energy) You can get the solar powered light with a small solar panel as well since they are not that expensive. Use the light as your
convenience to get into coop at night and be able to see. Do not expect egg production to increase with that light.
During winter my pet chickens have indoor housing inside my garage. I do provide them 12 hours of light on a timer since there is little outdoor light available for them. I also do provide limited heating, but only during severe colds, and I do not warm very much above freezing temperature. I think the light is there so they do not go wacky.

.. They see their food, and water and surroundings as well as roosts. Lites out and they go nighty nite.

Their laying during winter is extremely down. Laying resumes to normal when they go to their outdoor facilities in early spring.
Here is one for $20.
https://www.harborfreight.com/solar-shed-light-62549.html There are more options if you search the catalog. Nothing to break the bank.
WISHING YOU BEST and
