Many years ago now, I drew a tag for a goat in 323. It was the year before the big fires in YNP. If things haven't changed too much,,, you'll have no trouble seeing goats,,, you might have trouble getting the right circumstance to close the deal.
Getting snowed out in the middle of September was a blessing in disguise. I would have killed one that early if the opportunity had presented. I went up there with every set of days off. You could see the hair improve with every week. I still have a memory of watching a goat standing on a ledge in a cold hurricane force wind. Its hair parted by the wind straight down the middle. It was standing there like another day in the park. Most trips in resulted in a stalk on a goat that concluded with either no safe way to get close enough for a shot, or the time needed to get close enough was not available due to the shortening days.
A friend had the same tag the same year. We hunted together or separately as our work schedules allowed. One day in late October on a bitterly cold day our luck changed. As we got to the edge of timberline the wind was sucking the heat out of us, even as we were climbing ever upward. I put on the last layer of clothing left in my pack before we made our way to a ridgeline that afforded easier travel along it. When we gained the ridgeline we ate our lunch before deciding which direction each of us would travel searching for goats.
Almost immediately after parting, my friend caught up to me and said he had found two along the ridge. Both where mature nannies. We had by that time, decided a good nanny would suffice. Since he had spotted them, he shot first at the goat of his choosing and I shot the remaining one. Mine nearly fell into the Hellroaring drainage,,, which would not have been good.
That tag provided the most physically challenging hunting I ever experienced. I walked close to 70 miles in those mountains between scouting trips and hunting trips. I was pretty close to my physical prime. When I look at her on the wall,,I remember that there was a day that I could pull off that hunt.
We didn't have a camera with us on the day we succeeded. So it wasn't until I got home that we got a photo of my goat along with my son. Now he's older than I was then. Time flies.
Good luck with your tag. You can pm me if you like.