Line of Position
Do all observers see the sun at the same location at dawn?
Pretty nearly. It doesn't vary as much as I predicted from drawing 2 dimensional pictures of the 3 dimensional reality.
I collected these charts and tables on 11 September 2010, which is close to the fall equinox. At dawn, someone near Buffalo would see the sun at 83.1 degrees, which would generate LOP perpendicular to the sun sighting of 353-173. The sunrise azimuth at Howland would be 85.59 and 85.65 at Niku, giving a LOP of 355-175.
I don't know whether the difference is due to the earth not being a perfect sphere or solely to the difference in the latitude of the observers.