When Jupiter reluctantly climbs out on the branch of the tree he finds a skull. It is nailed to the branch in such a way that the face of the skull appears to be looking directly at him. According to the summary of the story in the eNotes Study Guide (see reference link below):
On the seventh branch up, Jupiter found a human skull nailed into the bark. Legrand directed him to drop the gold bug through the skull's left eye socket. The gold bug landed on the ground, Legrand marked its location with a wooden peg, and then used additional pegs to triangulate a spot some distance away from the tulip tree. The three dug a deep hole with the spades they had brought at the appointed spot, but they found nothing.
What went wrong, Legrand realized, was that Jupiter had dropped the bug through the wrong eye socket. He dropped it through the right eye socket because that was the socket to the left with the skull facing him.
Legrand does not require Jupiter to drop anything through the other eye socket, since he can easily revise his calculations to allow for the distance between the two eye sockets. They were only a few inches apart, but there was a huge difference when a line was drawn from the trunk through the spot where the bug landed and extended for a considerable distance.
Legrand later explains that it wasn't necessary to drop the bug through the eye socket, since the decoded instructions called for a lead shot; he just wanted to play tricks with his friend, who thought he was insane.