my understanding is that only two trees are allowed by the government to have the goats for conservation reasons. wanting the maximum revenue there are goats in the trees (both along route 207) all day long. although there may be animal comfort limitations on how long the goats can stay, i think there are several goats in the tree all day long. i'd say early morning for the light, but not too early as they won't put the goats in the tree until there's tourist traffic - on the other hand, photos of the goats going up the tree (and young goats-in-training being placed there would be interesting)
that said, there a a couple more goats in the photo above than when i was there mid April late morning