In neurophysiology we refer to "efference copy". In short, efference copy is when the brain area that sends a signal to cause a movement also sends some "copy" of that signal to the sensory part of the brain. This copy signal helps the sensory brain areas predict what to expect from your own movements, and therefore lets your perception be driven by changes in the world rather than your own self-motion.
You can also frame this in predictive coding models of brain function, in which brains are said to create model of the world and respond primarily to violations of this model/relatively unexpected events (for example, if a filing cabinet remains motionless in the corner, you don't notice it; your model is that filing cabinets are inanimate objects that stay still. If it moves forward a few centimeters, you will notice it quite quickly). A light flashing on and off is a somewhat "unexpected" stimulus: ordinarily, lights stay either on or off. However, if you blink such that when your eyes are open only when the light is on, nothing unexpected is happening to the light: it's on when your eyes are open, and you expect to see nothing of the world when your eyes are shut so the absence of the light with eyes closed is expected.
For another example that's easy to test out, if you move your head side to side, you won't perceive other objects as "moving" (the vestibular system helps inform this perception of the world as stationary as well, by measuring rather than predicting your head movement). You may notice that your visual perspective changes, but you don't sense that objects are really moving in the environment. Same when you change your visual gaze from one target to another: you'll blink briefly and the image that lands on your retina will be completely different from the one you just saw, but you still perceive the world as having stayed the same, not as if everything in front of you has just jumped by a meter or more.
Other applications include understanding why it is difficult to "tickle yourself", and how an echolocating bat can differentiate between its own calls and the reflected echos.
The Wikipedia page I linked to at the start has a lot more to say about efference copy, and you can also use that phrase as a search term to find out more about the specific circumstance you're describing.
