Egg laying "schedule"?
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We let our birds out in the morning and put them up at night, they lay whenever they want to (and some lay where ever they want too!) I don't think their outside playtime would really effect their laying habits, some birds lay early and some lay late. I've had birds lay the next day after they egg squat and others take weeks after the first squat XD
It can vary, some of mine dance, some go flat, but here are a few pictures of a basic squat <3