God, this thread just took up the best part of an hour in reading time and all the while my neighbours 'dusk to dawn' light has been twinkling away through my window.
That's not such a bright light though, all it really lights up is their own door, I can see it shining but not in a bothering kind of way. It comes on gradually at dusk, stays on all night and turns of gradually at dawn. Ours is motion sensored and lights up half the world for about a minute at a time, but only if someone decides to hop up and down on the garden path, waving their arms about and muttering "work, bloodly thing, work why don't you."
I think you've explained quite well OP that the light couldn't have been shining directly into the mans house but even so, I think you reacted in all the wrong ways too. You and he were both in the wrong. He should not have threatened you but you should not have attempted to provoke him further just to score a point in return.
We were kept awake last night too, by a house alarm in a neighbouring street, going off for about half an hour between 12:50am and 1:20am. It's been going off at random times for days, often late at night. I was sorely tempted to go and complain but wanted to avoid a situation like you have described so I have reported it to the Safer Neighbourhood team today instead.
It's horrible to be bothered by something like that, be it noise or light or whatever. And light does bother lots of people. We have blackout curtains because light pollution does stop me sleeping. DH can't even charge his phone in the bedroom because of a tiny green light on it that keeps me awake and causes my left leg to --accidentally twitch and kick him every so often until he turns the phone off 
Is it possible that his 3am threat would have been to call the police on you?
And is it possible that he was up watching television because he was in some way too bothered by your light to sleep?
Or perhaps worried about or intimidated by the presence of teenage boys in your garden and so not able to settle?
I know elderly people can sometimes find they are getting less sleep and they can become unnerved by a change from the norm. This, for him, might include a group of strange teenagers setting up camp in a normally dark garden now suddenly lit up for the second night in quick succession. He might have been concerned they would be camping out all summer long.
I agree with you, nobody is at their best at 1am whether they have just been woken up or have been kept awake and reached the end of their very short and rude tether.
He may have responded better if you had explained why the boys needed the light.
I don't think you should have called him ridiculous and told him to close his curtains, not when you had no idea which house he was in.
I think I would have called the police if I felt I, and more particularly children in my care, were being threatened in a vague but possibly serious way though.
You certainly shouldn't have kept the light on for a further hour just to prove a point. And if he hadn't complained, it would have been on all night, so you can't defend yourself to the people saying it was wrong to leave it on all night by saying you turned it off after an hour because you wouldn't have done otherwise (did that make any sense?)
I do think that this has been the sticking point for this thread. If you hadn't kept the light on to score a point I think you would have had a lot more sympathy.
The same goes for your reaction to the 'outcome' so far. Yes the police have been supportive of you and he knows that you won't take threats lying down. But you seem very gloaty in some of your comments (the "SUCCESS" one etc and all the "don't mess with me and mine" ones) and it makes it hard to see you as an intimidated victim of an unreasonable man.
I hope you're all having a better night tonight though. No alarms going of here (touch wood) so I'm off to try and catch up on my sleep too.