The correct answer is B) During the nighttime when the vessel carries overnight passengers. This is because U.S. Coast Guard regulations require that on small passenger vessels that carry overnight passengers, a watchman must patrol the vessel throughout the night to guard against and give alarm in case of fire or other danger. This is a safety measure to ensure the wellbeing of passengers during the vulnerable overnight hours when the crew may be asleep. The other options are incorrect because: A) is too narrow, as watchmen are required at night even if the rest of the crew is awake; C) is too broad, as watchmen are only required at night, not at all times outside normal work hours; and D) is incorrect, as watchmen are not required at all times when the vessel is underway, only during the overnight hours when passengers are sleeping.