Before it meant a quick look, a glimpse was a flash of light. The word comes from Middle English glimsen, meaning 'to glimmer' or 'to shine faintly', from a Proto-Germanic root *glim- meaning 'to shine'.
The shift from light to sight is intuitive. A faint gleam appears and vanishes — you see it only briefly. By the 15th century, the word had completed its migration: a glimpse was no longer the light itself but the momentary act of seeing it.
Glimpse belongs to one of the most striking patterns in English: the gl- phonaestheme. Words beginning with gl- disproportionately relate to light and vision — gleam, glimmer, glint, glitter, glow, gloss, glare, glaze. This is not coincidence. The pattern runs deep in Germanic languages and may reflect an ancient sound-meaning association predating the split of the Germanic branch.
The Dutch glimmen ('to glow') and German glimmen ('to smoulder') preserve the older 'light' meaning that English glimpse has largely abandoned. In those languages, the word still describes what the eye sees rather than the act of seeing.