There are inexpensive solar lights that will stay on a bit after dusk which doesn't really matter but the amount of light at roost height is the important matter.
He'll have better luck adding a light. But, it's cute that he's thinking and thinking of all possible connections. There is a lot of research on this topic.
Providing all else is fine, nutrition, etc.. He can stimulate laying by adding a light to the coop on a timer to come on about 4 AM. Are all their combs and wattles enlarged and bright red? That's the sign of sexual maturity.
How old are the chickens?
Playing the egg song won't stimulate ovulation. It was a good guess though. This time of year POL pullets take longer to start.
Though they sing the song in relation to laying an egg, it is actually a call to gather the flock together. Roosters will even do it if...