On the right you see part of me while I'm making saccades, that is rapid eye movements between two fixation targets. These targets are my own eyes, which I am viewing in a mirror. The movement of the eyes is quite obvious, wouldn't you agree?
[BTW: filming oneself single-handedly proved somewhat tricky :), and, yes, the head isn't quite steady.]
What to do
Now do this yourself – not taking a movie, but standing close to a mirror (nose nearly touching) and look to an fro between the eyes. Do you see you eyes move? I bet you don't! Although your eye movements will be similarly obvious as mine, you cannot see them. Have someone check – they will see it. Or take a movie yourself… Interestingly, the viewer of the camera was visibe for me in the mirror too, and there I did see my eyes move (more on that below)!
The surprising thing here is the absence of a perception, namely perceiving your own saccades. The mechanism behind this is called “saccadic suppression”; it is useful to suppress the motion blur during your saccades, which would be quite distracting were it not for saccadic suppression. The suppression is not total (different publications differ in effect strength between a factor of 3 to 10), but it is good enough, obviously. The duration depends on the size of the saccade, 50 ms is in the right ballpark.
So why could I see my saccades in the mirrored camera viewer? Because the viewer shows the image with a little delay, so the eye movement appears while the saccadic suppression is already over. This leads to the following additional experiment: If you have a notebook with a built-in camera, or a webcam, look for a program that will present its image directly on your screen (on a Mac you can use “PhotoBooth”). Now look from one of your pupils to the other: the eye movements are clearly visible now!