I believe we saw in TGS further thought-process by Rand on how to solve the "to live you must die"-Aelfinn riddle and possibly trick the Shadow. We already know from the previous books that Rand tries to figure out the Prophecy's meaning, especially with Alivia's help.

In TGS, ch. 5, Rand muses:
"Was this all he would leave to the world? A taint cleansed, yet men still killed or exiled for something they could not help? He had bound most nations to him. Yet he knew well that the tighter one tied a bale, the sharper the snap of the cords when they were cut. What would happen when he died? Wars and devastation to match the Breaking? He hadn't been able to help that last time, for his madness and grief at Ilyena's death had consumed him. Could he prevent something similar this time? Did he have a choice? He was ta'veren. The Pattern bent and shaped around him. And yet, he had quickly learned one thing from being a king: the more authority you gained, the less control you had over your life. Duty was truly heavier than a mountain; it forced his hand as often as the prophecies did. Or were they both one and the same? Duty and prophecy? His nature as a ta'veren and his place in history? Could he change his life? Could he leave the world better for his passing, rather than leaving the nations scarred, torn and bleeding?"

And when he watches normal people in the camp, Rand tells Flinn:
"For all their laws and oaths, they are free. Me, I seem as if I can do as I wish, but I am tied so tightly the bonds cut my flesh. My power and influence are meaningless against fate. My freedom is all just an illusion, Flinn. And so I envy them. Sometimes."

Furthermore, Rand muses in ch.22:
"To live you must die, the answer to one of his three questions. If he succeeded, his memory — his legacy — would live on after he died. It was not very comforting. He didn't want to die. Who did? The Aiel claimed they did not seek death, though they embraced it when it came."

And a bit later:
"There was a game children played, Snakes and Foxes. It was said that the only way to win was to break the rules. What of his other plan, then? Could he break the rules by slaying the Dark One? Was that something that even he, the Dragon Reborn, dared contemplate?"

While Rand would like to be free and trick the DO, Rand still considers that he will most likely die at TG. On the other hand, he fears that if he dies, all he built before will break again, because there will be a power vacuum.

In the end of TGS, Rand experienced again how liberating it is to be "just another man", when he disguises himself as a beggar. The next logical step, IMO, is that Rand will realize that he can't and doesn't have to lead the Forces of the Light through TG. His ultimate task is to confront the DO in the Pit of Doom, but he must learn to trust others to lead mankind.

Therefore I believe that Rand - especially to avoid a power vacuum after TG - will eventually hand his authority over to another powerful channeler, noble and former false Dragon, namely Logain, already before TG. Logain will basically become the "official" Dragon Reborn to the world (this is supported by Min's Viewings of Logain's glory & Ewgene's Dream of Logain stepping over a Rand paper puppet). Likely Rand will give Logain Callandor as well; a striking proof for mankind that Logain is indeed the DR.

BS indicated that there will be a last big meeting of the main characters before TG, probably at the end of ToM or the beginning of AMoL. The Pattern obviously wants that Rand meets the other two ta'veren yet again, Rand also has to marry his three women and see Moiraine again. All this makes it most likely that this last meeting will happen in Caemlyn. Besides the ta'veren, Rand's girls & Moiraine, one can expect that especially Egwene, Nynaeve, Tuon, Alivia and Logain will be there.

I believe that among this group of the most important characters in Randland, it will be agreed that Rand has to fake his death and that Logain takes the role of the Dragon Reborn, probably after a big battle at Caemlyn (one could proclaim then convincingly that Rand died during the battle).

Rand will probably be put into a temporal coma (the weave delivered by Alivia). Then there will be a funeral by his three women to make Rand's death more believable (that will most likely lead to the "three on a boat and the one who is dead yet lives"-scene, which Nicola foretold). Plus, Elayne will give Rand the dull dagger, which hides the possessor from the Shadow.

The reasons for this faking of his death is that Rand would in a way break the rules, because he officially ceases to be the Dragon Reborn in the eyes of the world. Secretly he is tricking the Shadow, though, since the Shadow will concentrate on Logain or already believe that the battle is won, although Rand will appear in the Pit of Doom at TG. That Moiraine was presumed dead by anyone could further inspire Rand to fake his death to act more freely against the Shadow.

Of course, to achieve this I think Rand has to kill Moridin before. But that should be possible using their link (Min had a corresponding Viewing). Most likely also Alanna will be dead or her bond to Rand severed at this point.

Thus, the former Dragon Reborn would die, Logain take his place, but Rand still live, and in the end be able to beat the Shadow. Of course, this doesn't tell us if Rand will actually survive TG (IMO, RJ will certainly let Rand live, after all he was through). However, by making Logain his heir as the Dragon Reborn, Rand would at least get the chance to avoid a power vacuum (which might lead to another Breaking) and to live a peaceful life again after TG without the burdens of a leader.