Time for some more rambling speculation...(spoilers for F&B and mild spoilers for the Forsaken chapter in Winds).

In George’s original outline Jaime is your typical bad king, a brutal and ambitious man who covets kingship and comes to power by killing everyone in his path. Of course, in the story we get, he's nothing like that, and instead that ambition goes to Cersei, which makes for a far more interesting story, given much of Cersei’s quest for power is arguably driven by her lack of agency in her own life, rather than just a manly Quest for Ultimate Power.

However, GRRM has another character who fits the original Jaime template, at least a little: Daemon Targaryan, the younger brother of King Viserys I, the second husband of Princess Rhaenyra, and (to quote GRRM) “a rogue if ever there was one”. If the histories are correct, Daemon is responsible for some pretty awful stuff, but there are some more nuanced and conflicting aspects to his personality too. As Measter Gyldayn says:

Over the centuries, House Targaryan has produced both great men and monsters. Prince Daemon was both. In his day there was not a man so admired, so beloved, and so reviled in all Westeros. He was made of light and darkness in equal parts. To some he was a hero, to others the blackest of villains.

This isn't the place to summarise all of Daemon's story, but suffice to say, he is a major character in the Dance of the Dragons, and one of its proponents. Hot tempered, talented, charming but also promiscuous and ambitious, he has some elements of Jaime, but also many that are literally the opposite. Daemon covets some of his brother’s power, and after his niece Rhaenyra becomes heir, he first tries to undermine that, and then seduces her, and later, after trying to make his own kingdom in the Stepstones, he returns, forges a alliance with her, and marries her. But that's all a story for another time, because I want to look at something, or someone, that happens later in his life: Nettles.

Daemon is one of the leaders of the Blacks, and one of the assets that Rhaenyra and the Blacks have is dragons. Unfortunately, what they don't have is riders. So they send out an invitation to those with Targaryen and Velaryon blood - "Dragonseeds" - to come try and ride a dragon. Lots of people die trying. But Nettles, a plain peasant girl, uses a clever method that shows a lot of perseverance (a bit like someone else's fighting strategy...) to form a bond with Sheepstealer, a dragon who had never been ridden before. Nettles, btw, is small, brown haired, brown eyed girl, with crowded teeth and a nose that had been slit (a punishment for stealing), who "could not be called pretty". She's also foul mouthed and daring. So, she's a little bit Brienne, and a bit her opposite, kind of like Daemon and Jaime.

Late in the war, Daemon heads to Maidenpool, taking Nettles with him. They use it as a base from which to search the Riverlands for one of the Green's more psycho partisans, Aemond, who is effectively Joffrey with a dragon, and is basically just prowling around on Vhagar, burning stuff. They spend a lot of time together, on their dragons, and Daemon comes to love Nettles. The nature of that love is subject to debate, with some speculating that the prince treated her as a daughter, and others (including the wiki) that he took her as a lover. The latter certainly seems far more likely. The rumours have them sharing a bath.

By this time, it is possible Daemon may have had something of a mini Riverlands redemption arc. The style in which F&B is written means you don't get the insight into the characters’ minds in F&B that you do in asoiaf, but he no longer seems to care much for the war he helped start. Meanwhile, an increasingly desperate Rhaenrya becomes convinced that all the Dragonseed bastards are traitorous and plotting against her. Rumours that her husband is shagging Nettles don’t help that paranoia. Rhaenrya sends a raven to Maidenpool requesting Nettles’ head and ordering Daemon home. The men there disobey and a maester warns Daemon. He and Nettles spend a final night together, and then the next morning Daemon helps Nettles saddle her dragon, before they part, each riding their dragon away, Nettles with tears on her face.

No word of farewell was spoken betwixt man and maid, but as Sheepstealer beat his leathery brown wings and climbed into the dawn sky, Caraxes raised his head and gave a scream that shattered every window in Jonquil's tower.

Daemon thanks the Lord of Maidenpool for his hospitality, and then takes Caraxes and goes to Harrenhal to challenge Aemond. He waits there for thirteen days, marking time by slashing a weirwood tree, until Aemond finally arrives. A one-on-one duel of that nature is suicide for Daemon, because Vhagar is so old and bloody enormous. Daemon knows as much, and so does Aemond:

Daemon: Were I not alone, you would not have come.

Aemond: Yet you are, and here I am. You have lived too long, nuncle.

Daemon: On that much we agree.

As they launch into the sky, Aemond straps himself into his saddle, but Daemon leaves his saddle straps unbuckled. When the dragons clash in the sky, Daemon leaps from his dragon onto Aemond's in mid-air, plunging Darksister into Aemond's eye. Vhagar and Caraxes kill each other. Aemond's body is found in the God's Eye, still strapped to Vhagar's skeleton (there is a super cool painting for June in the 2021 calendar - otherwise known as the "Jaime calendar"). Daemon's body is never found. Legends say he went to be with Neetles, "to spend the remainder of his days at her side." While even Mushroom dismisses those tales as impossible, the tone is such that we are cleaely means to think, or hope, it all very possible.

What does this have to do with Jaime and Brienne? Well, I don't know that you can draw too many parallels between Jaime and Daemon, but there are certainly some there, and I wonder if Daemon is GRRM's way of exploring his original conception of Jaime.

More to the point though, there are definitely some parallels between Jaime and Brienne and Daemon and Nettles. And so I wonder, if we are to give any credence to the show (I know, I know, why should we?), then perhaps what we will get in the books is an ending a bit more like Daemon's. Daemon leaves Nettles, and does his duty to his queen, dying in the process, but as sad as the story is, it isn't disrespectful of Nettles, or to the Daemon's overall journey. He takes out one of the worst of the war’s proponents with him, and there remains the possibility of a super romantic kind of ending, with the both of them disappearing. There are far worse endings than p something like that for Jaime and Brienne (albeit, given Brienne's other role as heir to Tarth, one would hope in the books that a mysterious man turns up on Tarth...worth noting that legends have Nettles becoming some kind of fire witch leader of the mountain clans in the Vale).

There is another even more speculative aspect too. While the obvious theory is that Jaime would go back to save Cersei (aka the show), or Tyrion, or both from each other, or something like that, Aemond offers another possibility: Euron. Granted, it is entirely likely that DnD just flat out made up Jaime v Euron because they thought Danebowl was funny, but there is also the possibility that it has some truth in it. This is particularly possible if Euron is a failed greenseer as per several leading theories. Bloodraven has taken an interest in Jaime and Brienne for some reason, so perhaps there is a reason (not to mention the parallels between Jaime and Freyr). And F&B provides another hint. When Daemon calls the duel with Aemond, Aemond arrives at Harrenhal with his pregnant lover, Alys Rivers. There is a lot of Melisandre in Alys, including visions and the possibility of some kind of murdery shadow magic. If Aemon's visions of the pale lady with Euron as indeed a suggestion that Mel takes the Crow's Eye's side ("beside him stood a shadow in woman’s form, long and tall and terrible, her hands alive with pale white fire"), then Daemon's ending may well be foreshadowing an end game showdown between Jaime and Euron.

Or it may not.

But in either case, the Daemon and Nettles story at least gives us a taste of George's idea of a bittersweet love story, and even at its most tragic, it is still deeply romantic.