I've wasted 20+ years and half my life's earnings leasing land in that area of Chambers/Lee/Macon and the truth is I don't know how you'd know when the "rut" is. If you put a gun to my head and said "give me a 10-day period that you're MOST certain of" or I'm gonna kill you, I'd tell you Jan 5th -15th is the most likely time to see what we call "the rut". But frankly you could hunt 5 years in a row and never see anything other than scrapes show up around early December (and literally never be touched again), a button head push a doe around in the powerline, etc. I could count on 1 hand the number of times I saw a "shooter" buck pursuing a doe (I won't even say chasing), and crap I saw them do it in October bow season, Christmas, March in turkey season, geez Louise who knows. I've seen bucks grouped up that showed no appearance of "rutting" on the last day of season. So if you have land in that region and you tell me that you ALWAYS see a strong and predictably defined rut the same time every year, then you sir have a friggin diamond in the rough and you better never get rid of that land. In total seriousness, maybe once every couple of years there would be a noticeable week (usually Jan 5 - 15 ish) when we'd see inarguable signs of chasing. But even then it wasn't strong enough to guarantee you a chance to shoot something.
Seriously, I'll always remember opening day of bow season one year (Oct 15th) watching multiple racked bucks absolutely trying to kill this poor little doe. They chased her for 30 minutes all over a creek bottom, buck roared, ran over bushes. And that was literally the ONLY even remote sign of "rutting" I saw that whole season (this was extreme northern Lee Co). Never even saw a spike sniff a doe in January.