In my area thr rut peaks about the last week of October into the first week of November.
From what I have read, the studies show that the two factors that influence the rut the most are the length of daylight hours, and the moon.
The last study I read said that the photo period is a stronger influence than the moon phase, and that the peak is within a 4 or 5 day window each year. From what I have experienced, this is pretty much true. I think that when the rut hits with a full moon, it appears "weaker" because most of the activity is going down at night!