I do beliebe I've learned the riddle by heart now, but I'm still no closer to the answer.
Alright. What can I come up with for terror's night? Off the top of my head, the death of the 2 Trees, and the darkness that Sauron sent out in preparation for the decisive battle. What could have enlightened anyone/thing at those times?
Death of the 2 Trees of Valinor: The Silmarili and the fruit of the trees, ie the Sun and Moon. But I have already guessed both. Wait... stars! But stars don't seem to make much sense with the rest of the riddle. I don't think anything was made lighter at that time, so that meaning is out. How about to make known? It's awkward phrasing, if that's the meaning, but there's one instance of finding knowledge, when Manwe looks from Taniquetil and sees Morgoth escaping in a black cloud. So is it possible that "to the third"=to Manwe, "enlighten the terror's night"="explain" (for lack of a better word) the reason for the darkness, "flight"=Morgoth's and Ungoliant's... but which is "I"?
Sauron's darkness before battle: too many and too few things that are involved with light. Phial of Galadriel? Therefore the "third" has to be Frodo or Sam, but the rest makes very little sense. Beacons? Can neither fly nor flee and are no mystery. The wind that blew the dark away? Ridiculous. Make lighter - Sam helping Frodo? Doesn't fit. Give knowledge? Faramir to Gandalf about Frodo? Then who are "you"? Everyone knows Gandalf. Plus, he's not some sort of mystery.
Just as a fun note, I=Gandalf and Other=Balrog, because, wings or no wings, they
did succeed in flying.