I'd guess a lot depends on the winter weather in your area. I believe the a good time to start listening would be when the gobblers start establishing dominance for the upcoming breeding season. They can make quite a racket doing this.

In many places the hens may be a bit aways from the bachelor groups of toms. If you can pattern some hens, you're one step closer to your goal.
One of the videos with "Wilbur & Cuz" shows an awesome turkey fight in Jan (in Mississippi?) Good luck next spring.