午 first drew a pestle for pounding grain, then was borrowed for the seventh Earthly Branch — the two hours around midday (11am–1pm) in the ancient 12-part day. The pestle faded; noon stayed.
午 slices the day: 上午 (morning — 'before-noon', with 上), 中午 (noon, with 中), 下午 (afternoon, with 下). 午饭 is lunch and 午睡 the sacred noon nap. In the zodiac hours 午 belongs to the horse, which is why 午马 pair up in fortune-telling. The Dragon Boat Festival, 端午节, sits on the 'upright noon' of the year — the fifth day of the fifth month.
The sun at the pestle's tip — straight overhead: NOON.
端午节 (Dragon Boat Festival) means 'Upright-Noon Festival' — the year's own high noon, on lunar 5/5.