That's a tricky one! Personally, I would say:
shine = something like metal, reflective surface. "The stainless steel shines in the light."
glimmer = makes me think of glitter
..but this isn't a verb I would use ever. The only thing I can think of is like a firefly that has a weaker light, "The firefly's light glimmered in the night sky."
gleam = also a verb I don't use much, but you might say "The floor was gleaming, it was so clean!"