There are three lakes lower red castle, red castle, and upper red castle. These lakes are accessed by the east fork of the smiths fork trial, at china meadows. You get to this trail head by heading south from mountain view wyoming. The goats i have seen were not on the mountian called "red castle" itself but on the cliffs on the other side of red castle lake (middle lake). Although there could be some on "red castle" but i've never seen them. I saw them at the end of Aug. I hope that helps.