The Eye’s effect only lasts until the end of the player’s own turn. It does not carry over to opposing player turns, and then has to be reset at the beginning of the player’s next turn, even if they do choose the same ability again.
On a related note, for win condition #3 on page 14, can the phrase “a player” mean the opposing player, or does every “his/her/player” reference in that sentence specifically reference the active player’s turn and no opponents?
I assume there is no way to eliminate the Wolves UT from the same ship that finds it on an island? I think the free explore would end before you could voluntarily shoot with a musketeer (if you had Captain), and a Marine shot would be a separate action from the explore that reveals the Wolves. (especially for initial discovery of the Wolves)