The motif of a glowing/shining sword is very old; for the flash of the brightly
polished sword suggested a flame to many cultures.
English "brand" meant originally "fire, blazing object,"
but early on acquired the secondary meaning of "sword." The same double
meaning is attested in Old Norse as well. In Genesis the cherub's sword
to guard the entrance to Eden is said to be a "sword of flame" -- i.e. "a
bright, shiny sword; one that shines like fire."
Of course, those are all just figures of speech: empty
rhetoric. In the same way in which Tolkien repeatedly tries to breathe
new life into worn-out figures of speech (he has a very literal "crack of
doom," e.g.), perhaps he decided to do the same with the "glowing brand/shiny
sword" image. His shiny swords would not just reflect a trite metaphor --
his swords would genuinely glow.
Also, in case no-one's said it, only Elven swords from the
First Age glow. After the First Age the Elves lost the secret for making
such swords. Narsil doesn't shine because, first, a Dwarf made it; and,
second, late Third Age Elves reforged
it.
