In Tormund's tales, he never speaks of sailing. The sea would make for some great stories for him. Yet, I like the concept of Tormund being Maege's secret lover.
Anyway, I came her to discuss something mentioned in the OP
Was it related to the truth behind Lyanna?
I think there may be a few ways that this could be true.
I've contended for fifteen years that Aerys is more likely to have impregnated Lyanna than Rhaegar... but either way, a Targaryen b****** (whom Eddard refused to murder) might be a huge political asset decades in the future or safely kept out of the way by putting him in the NW. Eddard and Ben may have conspired to care for Lyanna's son by Ben taking the black so that he would be a high officer or even Lord Commander when Jon would take the black after Eddard cared for him for his first sixteen years.
Did they really take care of him in this manner? Well, it's Catelyn's POV where Luwin says that Ben told him that Jon wanted to take the black. Catelyn thought Eddard was surprised. But we know she's susceptible to being manipulated by Tyrion, Robb, Littlefinger, Walder, and Jaime.... so mayhaps Ed and Ben concocted this (Ben pushed a drunken Jon into it) in order to appear they are innocent.
And then there's how Jon became a steward. Everyone knew Jon had extremely rare fighting skills upon his arrival. Did Mormont just pull him out to be his squire? I don't think so. Ben had a private meeting with the Old Bear the night before he left. I think Ben convinced Mormont to get Jon in line to become an officer. The irony is that Jon thought his meeting with Aemon to secure Sam's appointment, as a steward, was unique.
I do think that Ed and Ben saw the NW as a high and noble calling. They could not ask Robert to remove Jon's bastardy, but they could pave a path for a Targaryen b****** to still protect the Seven Kingdoms as LC of the NW.
On the other hand, maybe Ben did go to the Wall as punishment. From Meera's story of the tourney at Harrenhal, we can surmise that the Stark siblings were close. What if Ben had information regarding Lyanna's relationship to Rhaegar or her situation at court that was pertinent to her disappearance? What if he did not share that information as soon as he learned? What if this information could have prevented Lyanna's disappearance and death, Lord Rickard's death, Brandon's death, the deaths of Eddard's good friends, the deaths of tens of thousands, the entire rebellion, and the death of Eddard's secret love, Ashara Dayne? Given that Ben was fourteen years old (give or take a year) during the rebellion, how would nineteen year old Eddard have reacted upon learning the whole debacle could have been avoided by Ben's honesty?