The question makes no sense, unless you mean the light source is in movement, perhaps at the speed of light. In which case, the eye can determine displacement or movement of a small fraction of a minute of arc. . A fixed light, unmoving, travels at the speed of light; cycling off and on at anything more than 70 oscillations per second, the light would appear to always be on, because of the persistence of image property in the eye. This feature allows for the impression of moving neon lights in Vegas, as well as motion pictures. The fastest movement the human eye can perceive is many orders of magnitude less than the speed of light, across a visual field.
It would APPEAR to be on, when in reality, it would be flashing rapidly. Our eyes just can't see that fast, so it would just appear constant. Similar to wheels on a car, when they appear to be spinning backwards.
"Blinking at the speed of light" Turning something on or off does not move it, it can not blink at the speed of light, that makes no sense. The speed of light is a well, speed. You don't say blink at 3 miles per hour
I would think on...because my theory would be off is unseen and eyes react to light...not educated here on this but from noticing that our eyes follow light ( watching headlights from a passing car at night for example).....i would say the light would appear on!