I know some folks consider the "whitetail rut" to be different things. To some it is when they start seeking and harassing which in our area usually begins the week of Halloween with a disclaimer that I killed a real nice buck many years ago in a hard flat out chase that lasted a good 20 minutes before I could get an arrow into him on October 8th. Then again last year I actually had a real great buck (I killed him a couple week's later) that I actually had tending a doe on October 17th all around me but no good bow shot offered even though I tried one through the brush that never even spooked him... I killed him while he was "seeking" on October 26th. The seeking phase is my favorite time to hunt and coincides with our Muzzleloader season. Most of my Best Bucks have been killed the last week in October while rambling from place to place scent checking does to see how close they are...
The Chase phase for us is right around the first week in November and runs until about the 10th or so. This is the time when the bucks are super amorous but the does are not quite receptive yet. It's a very frustrating time for the bucks as well as for me. Deer running through the woods willy nilly but can't quite get them to stand still within 30 yards for a good bow shot. See a lot, shoot a little but can be a great time if you know to hunt where the does hang out. Sometimes it all lines up perfectly and you kill the buck of a lifetime but sometimes this phase is your "story" phase where when you get back to camp you tell all the unbelievable stuff that you saw that morning while on stand but couldn't get a shot
I notice the actual "Rut" which is actual breeding begins right around Veterans day and can run for about 2 weeks. It's feast or famine at this time of year with you trying to figure out where all the deer went you saw the week before. Lots of times they are pretty well locked down in the "bedroom" and not moving much at all. In this time frame I have noticed once a doe has been bred and the buck leaves her is the best time to kill him in that time frame. November 16th is the day my trail cams for the past 5 or so years have gotten pictures of great "stranger" bucks. He will start looking for another estrous doe immediately and if you can catch him looking or happen to have that doe around you somewhere your odds are good. Our rifle season always begins the Saturday before Thanksgiving and we usually see some of this activity at that time. We have 2 full weeks of rifle and the first week can be "fair" and the second week the bucks may not even be looking at the does because they are no longer in estrous and are more focused on food.
The next great time to hunt, at least for me, is right around the week leading up to Christmas. Most guys are out of the woods because they think it is over and it is cold. We are in Archery season again but there is a rifle Doe only season that begins the 16th - 25th of December this year. Does that somehow missed getting bred in first estrous and doe fawns on first estrous come back "in". I have seen some crazy stuff that week while nobody else is in the woods. I watched 5 giant bucks chase a 50 lb doe fawn all around me one morning in a WMA while I sat there helplessly since I was carrying a compound and somewhere between my truck and the tree I lost my release. I didn't realize it until I got settled in the tree after putting my stand up. I just decided to sit there and enjoy the view until it got light and then I was going to get down and ease back the way I came looking for my release. The deer had a different plan and I shot every arrow I had off my bare fingers with a 30" axle to axle bow at them. Finger pinch was severe and no matter how low I held ever arrow sailed over the backs of these giant bucks until I finally almost aimed to hit 6' closer than the actual deer was and got a brisket shave with my last shot...It's a great time to hunt and if you have any of your target bucks left and any of your buck tags left shouldn't be idle time for you...This phase usually last about 2 weeks and in our area and even though I dislike it a lot of our bucks get killed at this time by folks who are rifle hunting for a doe and just can't pass the big buck they see and then justify it by saying they didn't get a buck during the general firearm season so they were "owed" a buck...
All in all anywhere between October 20th give or take a couple days up until the last week in December you can get into some sort of rut activity in our area of the country with some definitely better times to hunt within that frame but you can't Kill them if you aren't out there. Great time to have time off available or be retired