This is one of those spots in the theory that I figured wasn't all that predictable. But I'm glad you asked, because I've been thinking on it, and I've come up with what I think is a plausible scenario.

I'd noticed while writing the theory that when Gawyn swears, it's in Egwene's point of view, but more to the point, she specifically tells him to wait until she can find proof that Rand did not do it.

Gawyn's perspective is different, though:



One means by which Gawyn might get his 'proof' is Ellorien. He might also get it from the others who supported Dyelin; Gawyn will know better than to trust the ones who supported Arymilla, with the exception of perhaps Sylvase (another possibility for chaos). None of the children were important enough to have a clue what was going on in Caemlyn at the time of Morgase's disappearance, nor were they necessarily old enough to understand what was going on any more than the adults did. That is how Gawyn, being a logical person and typically a good judge of character, will have to see it.

But Ellorien in particular does not believe that Rahvin controlled Morgase, so I see her as a very likely source for Gawyn's proof - Ellorien, the first to throw her support to Morgase, and surely her most loyal friend.

I have gotten the impression that the Pattern has been holding Perrin in the south just as surely as the Pattern drew Verin to Mat. Technically, she could have been lying, but I do not think she was. Things are getting quite dire. If Perrin and Galad go to Caemlyn, then Gawyn will learn the truth. But he won't, and he'll find a way to kill Rand.

I have begun to suspect that Elayne will not be in Caemlyn at all when Rand and Gawyn duel. There is an important event that is lurking on Elayne's horizon: she must claim the Sun Throne. There was heavy foreshadowing in The Gathering Storm and before that Gawyn has a duty in Andor, to his sister.

In Arthurian legend, the Battle of Camlann is sometimes precipitated by Mordred usurping the throne in Arthur's absence by seducing the queen, Guinevere. Elaine is like Mary as far as Biblical names go, but Elayne has Guinevere parallels for being Rand's queen. It is unlikely that Gawyn is going to seduce Elayne; however, it is quite likely that Elayne would trust him to watch the kingdom while she goes to make her claim in Cairhien.

Thematically, this all ties back to the end of The Fires of Heaven and the beginning of Lord of Chaos, when Rand has just conquered both cities, one by ousting a Forsaken, the other by breaking the Shaido siege at Cairhien (where Moiraine ousted a Forsaken from their own ranks). It was then that Rand announced who he meant to have the Sun Throne, with no real indication if that was what he had been planning all along (though it seems likely, especially considering that it seemed Morgase would rule Andor for many years yet at that point).

I don't believe that Elayne will take the Sun Throne - I think Moiraine will - but I do figure that her going to claim it is probably important, and probably ties into Moiraine's importance as well. There's also a chance there for Demandred to get in some Mordred-ish action by being in Cairhien (though he would be rather tall for a Cairhienin...so was Barthanes Damodred). Demandred has spied on Elayne in Tel'aran'rhiod, and he had the hots for Ilyena as well. It may be that Demandred has been posing as a Damodred all along, and just not one quite important enough to be seen on screen (we have only seen a few of them). But the Damodreds have been taking a few hits. Barthanes was High Seat, and then Caraline. Will she still be High Seat as queen of Tear? It seems unlikely. Moiraine has been eligible to claim the Sun Throne for all these years, but so far as everyone in Cairhien knows, she died taking out Lanfear.

Back to Ellorien, and specifically, what she believes:



I could give other quotes to emphasize the point, but one important one is this:


Not a word about behind the Dragon Reborn, either.

So, Gawyn will betray his promise to Egwene because he will believe that he has found proof. It seems unlikely that Ellorien would try to turn Gawyn against Elayne, but she is clever enough see the opportunity to make Elayne's life miserable by helping to turn Gawyn against Rand.

In any case, I don't think that Elayne will be there to interfere when Gawyn and Rand duel, and it may well be that they duel in the exact same hall where Elaida gave her Foretelling, saying that Rand stood at the heart of the pain and division that come to Andor, and to the whole world.