One reason I have a problem is that you seem to contradict yourself.
For instance, in your description above your eyes clearly look directly along the line to each edge, like sighting a rifle (you're not seeing each line "from the side" like Mirza's clock example). But you previously said "No, it's not like sighting a rifle".
And, by the way, it's usually impossible to do what you describe with a CTE line and an aimpoint line because they don't cross.
pj
chgo
Pat, you don't stand directly behind either line.