First a disclaimer: this technique only makes sense in an open field where nearby hunters can easily determine that the situation actually involves a hunter and not another turkey. Personally, I don't see how this mistake could even be made, but better safe than sorry.
The reason this works late in the season is the foliage is taller and thicker and the wild turkey hierarchy is well established—meaning gobblers don't tolerate newcomers very well.
The ideal situation is sneaking in on two lone longbeards—they will surely investigate.
Go slow, stop every ten yards and slightly spin the fan, as if it were a pirouetting gobbler, go another ten yards and repeat. But, the key is to "appear" from a long distance so the targeted birds have time to accept the fact that another bird is approaching. Once they recognize it, they don't seem to care much about details.
Conversely, I f you show up too close, they'll likely inspect the situation more thoroughly and bust out of there. But, as with most aspects of turkey hunting, it may take a few tries before it works out.
I'll say this much, it is a tremendous rush to shoot a charging turkey—very exciting!