The hours I have spent having random late night conversations with my closest friends (and every now and then with a stranger) have given me an insight into them that otherwise would have taken much longer to discover during our friendship.

Years ago one of my best friends' RR and I sat on the roof of his 4x4 on the beach in the middle of the night and chatted until it was well past my curfew and I ended up sneaking back into the house. We haven't had a chat like that in years now but THAT was enough to keep us going more than a decade later.
I haven't been in a relationship in a while now but when I used to be - the late night conversations were always there (on the phone or in person). I remember when I left for university, my then boyfriend would call me despite the 13 hour time difference and we would chat until one of us dozed off before cutting the line. I don't know if people do that anymore - I hope they do because there's something really special about it.
I guess what I'm trying to say is that - if you haven't really spoken to someone well past the hours of midnight - then you haven't had a really deep conversation with them. There's 'day time' chats / social chats at parties etc but the 'real' conversations only happen when two people have time .. and that tends to be at the end of a long day .. Believe me when I say this - but you will discover another side of a person whom you know ... Am curious to know your thoughts on this ...