We had a rooster and he crowed at 2 am not just day break.
Established wisdom is that they all do it to proclaim their territorial rights. The dawn chorus is always the males.
Birds sing to show how they feel and roosters crow to wake people ans other animals in the mornings
My rooster crows endlessly from 11:00 p.m. To 5:00 p.m. !!!
Well learned one, Roosters crow in the morning so they may alert the birds so they will know it is morning and time for them to sing.
Ascribing any particular motivation to something or someone other than yourself is always tricky business. Perhaps birds sing in early morning because the ones that didn't never found mates. The air is still and sound travels far at that time of day.
Perhaps for the same reason, we don't hear it so much at other times of day.
Roosters crowing at daybreak are doing exactly the same thing as all the other birds that join in the dawn chorus, They are all proclaiming their territory and their maleness.
Many people get annoyed at roosters yet delight at the dawn chorus. Personally I find roosters a natural wonderful enjoyable sound which I can smile to, enjoy, ponder on and "switch off" and go back to sleep. What does disturb me are all the unnecessary loud sounds such as noisy neighbours, car horns blowing, engines left revving, drunks shouting and swearing, loud street arguments, loud music, night planes and all the rest of it. I think that the sounds of nature are wonderful.
I just figured they make noise when the sun comes up because they are either happy it is daytime again or maybe they think their songs and noise coax the sun to come up more and more - kind of like a rain dance of sorts :)
Our roosters start at exactly 5 am. Sun or no sun. Then all day long, LoL. I call them retard-chickens. If they hear another, they start. Just like a dog.