I found while hunting my goat in 2013 that when they were in their escape terrain it was very easy to get close to them and that the terrain they chose made it easy to stay hidden until very near the animals. Now this is obviously dependent on the mountain you are on and the your ability to navigate that particular selection of terrain. I can think of three instances when I was within 7 to 15 yards of the animals when trying to identify sex. After pushing them two or three times they would disappear into unnavigable terrain.
On the other hand a lone billy I identified on an open grassy slope (not escape terrain) ran after only a small glimpse of me at +600 yards.
Goats look at ya and wonder if you're dumb enough to come up there.....Question is....are ya???