To shine brightly with a steady light or a brief flash of light.
From Old English 'gleam' (brightness, light), possibly related to 'glow.' The word has maintained its meaning since Old English times, appearing in Beowulf and other ancient texts.
A 'gleam in the eye' is actually a real optical effect—the eye's curved surface reflects light, and large pupils magnify that gleam. Medieval people weren't being poetic; they were describing observable biology.
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