As far as I know, it's around the middle to end of September.
Those speedgoats get kinda weirded out during that time. I had one try to chase me away from his turf one year. I was blackpowder hunting deer in Nevada and just walked out of some high bushes. There was a buck antelope on the hill about 150 yds away. The 'ol goat looked at me and kicked and stomped and pissed all over the place. He would come at me about 25 yards, then stop and have his fit again..each time getting a little closer. At about 50 yds I was trying to think of how I was going to explain this one to the fish and game after I had to shoot him in self defense....LOL
I think maybe he didn't identify me with all the camo and junk I was wearing. He eventually ran off a ways and tried to stare me down from a safe distance.
Another friend of mine had one come after his orange Datsun pickup one year during the rut. Have fun...but be careful..they do get goofy.