It is not just a "path of the sun" problem with the bipolar map. There are times of day when both eastern Asia and the United States are in daylight, and Europe and Africa are in their nighttime. How do I know? I speak with clients all over the world and so am very familiar with time zones and when I can and cannot reach a client from here in the US. For example, right now in March, when it is 3:00 pm in NYC, then it is 4:00 pm in Buenos Aires, 6:00 am in Sydney, 7:00 am on the Kamachatka peninsula in Eastern Siberia, 8:00 am in Auckland, 9:00 pm in Madrid and Cape Town, 10:00 pm in Moscow, 3:00 am in Beijing, and 12:30 am in New Delhi.
In order for that to work on the bipolar map, the darkness of the night would be located in the middle of the map slicing diagonally across Africa and Europe and much of Asia (but not all of Asia), while the left and right sides including North and South America, Hawaii, Australia, New Zealand, and far eastern Russia would be in daylight. Japan and China would be in darkness while Australia and Eastern Siberia would be in daylight. That would be quite a trick with just one Sun. Really, how do Australia and Eastern Siberia manage to be in daylight when China and Japan are between them on the map and yet would be in darkness?
Maybe there are two suns...and the reason we can't ever see both at the same time....is.....because.....?
Actually, the more I look at the map, I see that the area of daylight forms a very large circle that encloses the area of darkness on the map....how the heck would that work?
At least the unipolar map does not have this problem of a circle of sunlight enclosing an area of darkness.
PS: It is also daylight on Wake Island, but I am not sure where that appears on the bipolar map. It is located east of Japan. But if it is on the right side of the bipolar map, then it clearly completes the circle of daylight surrounding the areas of darkness on the bipolar map.