easy. take pen and paper. draw a line of an inch exactly in the center. now rotate the paper on its center. the line rotates.
now draw a similar line but way next to it, near the edge (to make the effect more pronounced). rotate it on the paper's center as before. while the line in the center rotates, the line on the outside almost makes a looping / jumps rather than rotating.
the smudge on the window therefore needs to be super symmetrical in the center if it should have caused the glare during the rotation. if the smudge is more to the side, the glare would have done a looping / jumping rotation.
do you understand what i mean?
I do not accept your "the smudge on the window therefore needs to be super symmetrical" deduction. I don't even think your pencil line is an satisfactory analogue for a "smudge". Repeat the experiment with a big splash of tea on your piece of paper, rather than a small precise line, and we might have something closer to an analogue, and we might end up with the alternative deduction "the smudge on the window therefore needs to just be taking up a reasonably large area in front of the internal optics", which is a demand of almost immeasurable triviality.
Remember - Mick's already demonstrated that an imperceptible smear on a slide can mimic the effect seen - how is your pen line an analogue to that situation?