Tom,
Let me clarify my 12:00-3:00 reference as the position of 12:00 changes depending on where an observer is on the plane. On the FE monopole map, longitude lines emit radially from the north pole. Taking an observer closer to the pole than the equator, when the new moon passes the longitude line of the observer, the observer will be looking directly south with south being 3:00 from the pole and the sun being at 12:00.
I apologize for having to use a round earth model for number purposes but the general idea remains the same. Using a RE map, and I'll use rough locations since it's difficult to pin an exact longitude from a representative world map.
At Los Angeles. New Moon at approx. 120 deg. W sun at approx. 150 deg E.
At Tokyo. New Moon at approx. 140 deg. E. sun at approx. 50 deg. E.
At Greenwich. New Moon at 0 deg. sun at 90 deg. W
The point being, that at each location, the new moon-sun relationship doesn't change. It can't in a FE model. As such, the ambient light surrounding a new moon, be it some shade of light or dark, must remain constant for every new moon at that location. You can't have a both a day 1st quarter and night 1st quarter at Los Angeles since the sun and moon will always be in the same location relative to L.A.