Where we hunt pronghorn in the southwest part of SD near the WY border, the rut is usually around the last week of September-first week in October. WY hunting season is just prior and sends many pronghorn our way. Then they go back. At least that's how it looks to me.
If you're lucky enough to be on private land and can leave your stand up during the off season you can tie an old piece of cloth or something of the sort to your stand. I like to use an old camo bandana that I have. That way the deer get used to the movement and eventually don't bother even looking up when there is slight movement. This may just give you the time to draw your bow or raise your gun without being detected.