Would flying during a solar eclipse be considered night flying?

If a student were to go flying while a solar eclipse took place, would it be illegal? (due to it being dark)? Also, if a pilot landed during an eclipse, would it count as a night landing? As the FAR/AIM says that in order for a landing to count as a night landing, the pilot must land "between 1 hour after sundown and 1 hour before sunrise", and as a solar eclipse wouldn't count as nighttime, landing DURING an eclipse it might not count. But then, a student pilot could fly legally for the few minutes it gets dark. (I'm not sure how long an eclipse would last).