Where rare birds go, camera-toting enthusiasts tend to follow. But sometimes, all it takes to cause a commotion is a relatively common, though little-known, bird with some funky dance moves. On Friday, more than 650 people congregated for a special bird walk in New York City’s Bryant Park, where American woodcocks have been stopping to rest and refuel on their migrations north for breeding. “We had to have bird security manage the crowds,” Gabriel Willow, a naturalist who leads bird tours in...