“Gleam”, distributed fairly evenly throughout the work, is related to “glimmer” and “glimpse”.  The root *glim- can be found in glimmer, glimpse, glim (brightness).  It’s a ray of light or even of radiant beauty.

• 01.075 There many a gleaming golden hoard
• 03.001 and behind its shoulders the tips of snow-peaks gleamed.
• 04.041 It burned with a rage that made it gleam
• 05.126 and his eyes gleamed cold
• 05.127 in the gleam of his own eyes,
• 06.052 but you could see his eyes gleaming
• 08.005 and when it was Bilbo’s turn he would see gleams
• 08.005 and sometimes they would gleam down
• 08.071 Their gleaming hair was twined with flowers;
• 10.020 The gold gleamed on his neck
• 11.029 there was a gleam of yellow upon its far roof,
• 11.032 A gleam of light came straight through the opening
• 11.037 The gleam went out,
• 13.009 There was not a gleam of light –
• 13.017 a twinkling gleam showed them returning,
• 13.019 the same white gleam had shone before him
• 17.050 with a gleam of chill flame,
• 17.055 in the gloom the great dwarf gleamed like gold
• 17.062 Seeing the sudden gleam
• 18.032 that it gleamed ever
• 18.053 snow yet unmelted was gleaming pale.

“gleam, n.” OED Online. Oxford University Press, March 2015. Web. 11 May 2015.