Most of my kills have been morning kills, anywhere from sunrise to 10 am. Last years solid 9 was about 10 minutes past sunset, but I watched him for 20 before I got a decent shot. Given with a grain of salt. My stands are set up on travel corridors, not food sources or bedding areas. The time of my success varies widely with changes in daylight, temp, barometer, etc. quite frankly if I had them patterned to the minute, I would lose interest.
The best time to be in the stand during the rut is every chance you get. I will continue to get to the stand before daylight most of the time. There are some times though, later on in the rut that I feel like I'm better off coming in and hunting from say 9:00am to 2:00pm to catch that late movement. I let my trail cameras tell me when it's time to start the late morning hunts.
Two years ago I killed my second largest bow buck about 20 minutes into legal light. Like others have said, I try to spend as much time in the stand as I can especially during the rut! Personally I'd rather be setup before daylight instead of walking in after it's light.
Depends on access for me. I have one spot that I absolutely refuse to go in before first light unless the conditions are right. I will hunt my way into it right at sunrise, but it is a VERY short hike. Just about any other time I get in as early as I can.
Anytime in the woods during the rut is a good time. However, I do have a couple spots that I tend to go in a little late. Just because I normally do not see deer until after 8am. It just works out that way based on the lay of the land and where the deer are traveling from. Learn the area and you will learn when its best to hunt. **But........ I've learned that when you think you got them figured out. They make a change and do something completely different.
During the rut, I'm a daylight to dark guy. I want to be in the stand a half hour or more before sunrise. Depending on the stand and how far I have to walk to get it, how cold it is, etc., I'll eave the truck an hour before daylight. If its cold, maybe a bit earlier yet to avoid getting over heated.