Most of this story is mostly true most of the time.
Fitz isn't really sure why he's stayed with the Doctor as long as he has. It's not like he's never run away from anything before, and he's free to leave any time, but for some reason he can't quite bring himself to go. It might be because the Doctor needs him, or because he needs the Doctor, or maybe it's just because he's been away for so long that his normal life in London feels like a dream he once had, a reality away.
He tries not to think about it too often or too hard because it raises questions he doesn't really want to answer. So he sticks around and says goodbye to a lot of people (or carefully doesn't, as the case may be) and plays his guitar.
And whenever he does stray a bit, he always comes back.
It takes Trix leaving for Fitz to finally start to worry. He's known for ages that things are bad and heading for worse, but it's not until he and the Doctor are alone on the TARDIS and the silence feels like it could stretch on into forever that he thinks he might be in a little over his head.
The smart thing would be to leave, too, and he and the Doctor both know it even though they never say anything. But Fitz is really good at doing stupid things that turn out more or less for the best, and it's way too late to do a runner. More than that, the thought of the Doctor left all alone to face what's coming (Fitz doesn't know what that is, exactly, but he's dead certain it's going to hurt like hell) makes his stomach twist like he's going to be sick.
It's not like he has a life to go back to, anyway.
Sometimes, when Fitz has too much time alone with his thoughts, he thinks about Father Kreiner, and all the countless other possible incarnations of himself, and he wonders what that means for the him that's in the here and now (wherever and whenever that is). It's not a good idea to follow those thoughts, though, because they never lead anywhere good, and whenever he does let them go too far it's all he can do to sit on the floor and hold his head in his hands and shake. He's just one insignificant human fighting in someone else's war, and all he knows for sure is that he doesn't want to die.
It's not until the Doctor kisses him for the first time (and means it) that he realises the end is coming.
When it gets to be too much for him, which happens a lot, Fitz hides out in his room for hours and plays his guitar. Those are the days when he's most desperate for a cig, but he ran out some indeterminate number of weeks (months?) back and it's not like he can ask the Doctor to make a special trip just so he can pick up some more. It's probably a good time to try quitting, anyway.
So he sits on his bed alone and plays arpeggios, because they're simple and the repetitive motion is soothing, and tries to keep his mind on the immediate. It's when he starts to worry about what they're doing to Time and what Time will eventually do to them in return that it gets a hell of a lot harder to cope and his chest tightens with a feeling that's both more and less than fear.
He won't say it out loud, because the Doctor doesn't need to be told and saying it won't help, but he knows that there's no way anyone can win this war.
Fitz doesn't really get a chance to say goodbye. He's not as surprised by this as he wishes he were, and he's so tired that he can't even be angry with the Doctor for leaving him behind. He'll be angry later, maybe, when the white noise roaring in his skull quiets down and he starts to feel something other than numb (shell shock, he thinks, remembering another lifetime and a simpler war).
Time doesn't leave physical scars, but he's different now. He's not sure yet if it's the war that changed him, or if it's just what happens to people who spend too much time so far away, and maybe he'll never know. Maybe it's just something that is. What he does know, in an abstract sort of way, is that he can't stand on a London street corner forever. It's not the TARDIS, or the universe, or Time, but it's somewhere and somewhere, Fitz is coming to realise, is better than nowhere at all.
He's been gone a long time, and London doesn't feel like home anymore, but that might change someday, when he's had a chance to think about what's happened to him and mourn for what he's lost. And even if that never happens, he knows he has to give it a go.
The Doctor would be disappointed if he didn't and, even though Fitz knows he'll probably never see him again (and he hopes one day it'll be easier to know that), he'd hate to let him down.