One can easily end up hunting for these flashes of insight, to call it that, these glimpses of light that seem to come from nowhere. All understandable. Perhaps it is better to think of brilliance as part of a continuum; or simply as itself, manifesting when it sees fit to do so.
As usual, poets have been here before us. T.S. Eliot has a formulation that keeps popping up in my mind as I ponder this theme: "The surface glittered out of heart of light" (Four Quartets, "Burnt Norton" I).
A sentence that has trailed within me for a while is this: "Resting in the unknown". Sits perfectly with me.
A piece of music I often think about when the theme of brilliance/y crosses my mind, is Stravinsky's Petrushka, played on the piano. Underneath is a brilliant (!) performance by Maurizio Pollini.