What is the best way to hunt a buck that is mostly nocturnal?

A spotlight! No, seriously early and at last light. During the peak of the rut, hunt as much as you can, because that is your best chance of catching him out in legal shooting hours.
Also, if you can find his bedding areas, hunt as close as you can without spooking him. Even mostly nocturnal deer move some during the daylight hours, so be as close as you can get!

You could try to ambush him in the early morning, just do a little tracking to find out where hes going and how hes getting there or you could try the last light when hes coming out.

He has beenusing a grown up 5 acre field for the past 6-7 years.
I have only seen him twice.
Once he was a blur, and once it was at low lightI could barely see him.
The main four wheeler trail goes through the middle of the field so he never goes out in daylight hours.
I have yet to find his bed.

KT, if he's nearly that old, he didn't get that old by being stupid!
As I said, you'd probably have to find his bedding area and hunt early and late to catch him.
Older bucks can sometimes be almost un-huntable!
On the last place I hunted, one hunter had a stand on a good creek bottom, and he never even knew this buck was there! The buck had a bed right near the logging road, about 30 yards from where this hunter went into the woods! The buck would probably just lay there and watch the hunter go to his stand!
I saw this buck twice. Once one afternoon while bow hunting, and then again the very next morning! Both times he came within 10 yards of the logging road, stood a while, and then he'd turn and go back into the thicket! Had I been gun hunting I'd have had a shot, but he was much too far for a bow shot.
I relate this to make the point, some big, older bucks are nearly un-huntable! But theres always a chance they will make a mistake! Usually very early or very late! Good luck!

id have to say patience and persistence. those old mature deer are very hard to hunt. I have had encounters with a few and have never seen them again but I stayed on stand and hunted when I could in hopes to get a shot. but thats hunting

Contrary to popular belief, there is no such thing as a deer that is totally nocturnal. Their metabolism dictates that they feed every 4 to 6 hours. It aint easy but hunting very carefully in his bedding area during the mid-day is what I would do. Just don't make a mistake or you'll never see him again.

Crowd his bedding area. Carefully!

I agree with everyone so far. Also, you may try to hunt the Does in that area. Don't shoot them, but pattern them. Find out where THEY bed down at, and where they like to travel. Then place your stand accordingly, and during the rut, stay in it all day! Some bucks, we just never get a shot at, but that's what keeps you coming back time, after time. One day during the rut, he may just make that one mistake, and hopefully, you'll be there. Good Luck!

my guess would be late night like 30 mins before last light and first thing in the morning. Try to get close (within 100 yds) to his bedding area if you can.