These words are very similar and many can be used interchangeably; however in literature one words may be favored over the others in certain context.
Shining - smooth surface that's so reflective that you can see your face in it. "She looked at his shoes only to find her face shining back at her"
Glimmer - a faint, steady light. It's used when you can just barely see a light source. "I saw a glimmering light at the end of the tunnel." "She knew she was home alas when she saw her houselights glimmering through the fog."
Glistening - faint varying glow, or reflection due to water/moisture. "Fear caused his face to glisten with sweat."
Sparkling - sharp/brilliant light reflections that move around and vary in intensity. "She had never seen a dining hall so luxurious with sparkling chandlers and enough gold to suit a king."