On the right you see part of me while I’m making saccades: rapid eye movements between two fixation targets. These targets here are my own eyes, which I am viewing in a mirror. The movement of the eyes is quite obvious, wouldn’t you agree?
The interesting thing here is the absence of a perception, namely not perceiving your own saccades in a mirror under normal circumstances. The mechanism behind this is called “saccadic suppression”. This mechanism 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 studies 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 can you see your saccades in the camera selfie? Because the viewer shows the image with a little delay, and consequently the eye movement appears on the screen while the saccadic suppression is largely over.
I purposefully wrote above “current consumer video methodology”, because the delay will become shorter in future (“current” was 2012). I hear that, e.g., the iPhone X is so fast that the delay is too short make the saccade visible; this will apply to more and more smartphones over the years. What you can do there: film yourself while looking into the mirror, looking from eye to eye. The movie will show your sakkades, which are invisible “live”.
Wikipedia: Saccadic Masking
Idrees S, Baumann MP, Franke F, et al (2020) Perceptual saccadic suppression starts in the retina. Nature Communications 11:1977