The symbol never remains lit permanently regardless of whether or not they are in possession of the Triforce though, so that's irrelevant.But his hand only glowed when the mark actually appeared in AoL and SS; it quit glowing shortly after he proved himself worthy of having the Triforce. Also, I'd like to point out, on the Tapestry depicting the events, there's a very faint yet apparent (in the cutscene) Triforce under Zelda's "light." If that isn't apparent, I don't know what is.
And as I pointed out previously...
if Zelda had proven herself worthy to possess the Triforce of Power, then it could have passed from Ganon to her on it's own, which would have allowed her to obtain the complete Triforce