This goes back to GoT Bran I. Ned asks Bran if he understands why he had to execute Gared, a man of the Night's Watch.
"He was a wildling," Bran said. "They carry off women and sell them to the Others."
His lord father smiled. "Old Nan has been telling you stories again. In truth, the man was an oathbreaker, a deserter from the Night's Watch. No man is more dangerous. The deserter knows his life is forfeit if he is taken, so he will not flinch from any crime, no matter how vile. ..."
Jon was executed for being an oathbreaker; for planning to leave his post; for becoming involved in affairs of the realm instead of remaining neutral. And for making peace with the Wildlings.
But this could be inverted quickly; with the assassins as traitors. Depending on who holds the power. And whether or not Jon Snow still considers himself bound to his oath and the Watch.
There is also the battle at the Tower of Joy or trial by combat seems more likely to me. These matters of honor could have something to do with broken pledges. Perhaps Ned is an oathbreaker as well. But that is stretching it with nothing whatsoever to back that up.
Reading the Mercy chapter; Arya may break some promises as well.
Petyr Baelish? What would Brienne do to an oathbreaker when she finds out how he betrayed Sansa?
If they show the tower of joy, I expect a Kingsguard to be an oathbreaker.
That is exactly what I'm expecting too. I think I've read and agreed too much of your project, because I really think the oathbreaker is going to be Arthur Dayne.
I would actually hate it if they do the presumed tower of joy scene instead of keeping it as Ned's fever dream, unless the men aren't Dayne, Hightower, and Whent....well, Whent would be fine, who cares about him...anyways, the way The Queenmaker chapter seems to read is that Arthur Dayne defected while leading the etachment that Aerys II sent against the Kingswood Brotherhood, and that Hightower may have actually been killed during the attack on Elia's. So, I'm wondering if their absence was hidden? If they were actually killed prior to the Rebellion, then that could be one explanation for Ned's "where were you guys?" line of questioning.