We had our light on a 12V timer with a battery- you might need two batteries so one can be charged or you may be able to charge a small one during the day. The light came on in the morning. At night they were allowed to go to roost naturally, so could find their perch as it became darker. Big problem was the mess. They need food and water as soon as they wake and that means a lot of moving about and scratching at bedding, churning it into a poo filled stinky pile and throwing it into the feeder and drinker. so a lot of cleaning up every day and in the end we decided the extra eggs were not worth the effort. They need time off laying anyway- at least two weeks.
If you don't provide food and water during the extra daylight they will not lay because they need the extra time you provide to eat and digest sufficient food to keep warm and lay eggs.
Just use some 12V LED caravan lights.