A glimmer of something is a faint sign of it. Despite an occasional glimmer of hope, this campaign has not produced any results He is celebrating his first glimmer of success. to shine with a light that is not very bright = gleam
If something glimmers, it produces or reflects a faint, gentle, often unsteady light. The moon glimmered faintly through the mists. the glimmering ocean
shining softly and intermittently; "the glimmering mist of a spring rain splashed by sun and streaked by rainbow"- Claudia Cassidy; "glimmering candlelight"
A glimmering of something is a faint sign of it. a glimmering of understanding. the first glimmerings of civilization. a small sign of thought or feeling