Snopes tackles the urban myth that the presidential seal’s eagle changes it’s facing during time of war — to look to its left (audience right) at the arrows it clutches, vs. toward its right (audience left) at the olive branches. Most recently, it showed up in Dan Brown’s 2002 novel, Deception Point, and was also raised on The West Wing.
It turns out that in 1916, Woodrow Wilson changed the Presidential Seal (Flag) to be different from the Great Seal of the United States, the eagle of which has always faced the olive branches. In 1945, shortly after the war, Truman ordered that the Presidential seal be changed back, acknowledging the symbolism of the olive branches as a hope and drive for peace. Aside from those changes, though, there’s been no automatic pivoting head as a weatervane of hostilities (though that would actually be kind of cool).
And now you know.