I too have a goat permit and have never hunted them.
From what I've seen, yes the Billies are in small bachelor groups or solo this time of year. I'd expect them to start coming together mid-October or so.
I read that the rut wasn't until late October or November which would make sense. Because of where these things live, giving birth later in the spring would ensure higher survival rates.
They share the same environment and move around quite a bit but in the same "general" area. A place that has a billy standing in it today may be totally empty or full of kids and nannies the next day.
Good luck on your hunt!
"The shot you get will be during the last five minutes of the last day under the worst circumstances you can imagine. And you'll take it."