Good questions....
Here is another picture. I was looking at the projector from the side, in a dark room. I was in the room for about 30 minutes, and the same phenomenon was experienced every time I tried it.
No, let me try to explain a little more. I don't think it has anything to do with the eye lashes. Why? Well because it didn't ONLY happen when I would blink. If I was looking at something else, then really quick glanced at the beam of light, and then glance away, the spectrum would appear. If my eyes stayed fixed on the beam of light after first glancing at it, the spectrum disappears instantly. I would then do this over an over. My head was faced away, and I would move my eyes to the beam of light, and away at very fast speeds. Doing this allowed the image to come into perception each time my eyes looked at it.
Now another note, the spectrum I saw wasn't a perfect rectangle. However the spectrum was vertically aligned, as shown in the picture. So the banding, to answer your question, was perpendicular to the axes of light travel.