Nathan Stark isn't dead, but he isn't really alive either. There is one place in all of time and alternate dimensions that he is safe and sane. He can still watch over them, his friends, his family – but he can never be seen, can never answer them though he hears. Sometimes he thinks its better that they don't know he's out here, with the Doctor, certainly it's some kind of twisted torture or cruel punishment, demanded of him by fate. It isn't that Stark doesn't like the Doctor; he's a fine…man? Well, he isn't human, whatever else the Doctor is, but he has morals and a life with a past that is so painfully real that Stark can see it written in the Doctor's features though he's never seen any of it, really, despite what the T.A.R.D.I.S. can do. Stark won't ask to see it, because what he sees is enough.
It took a while for the Doctor to get used to him, and even longer for Stark to get used to the Doctor, what he was, and where he was.
And that, however long Stark may live, he can never go back. He is Nathan Stark and he is immortal, but he isn't flesh and blood, he is energy and elemental. He's made of the stuff of the T.A.R.D.I.S., the Doctor says, and it's the only the Doctor and the T.A.R.D.I.S. and Nathan Stark who have that kind of energy, so it's natural that they are drawn together, as the Doctor said.
Nathan Stark wondered if it wasn't something else, something about the Doctor, because he can't deny that his curiosity to unravel a puzzle became a pull to make the pieces fit and feel. The Doctor takes him places, places that Nathan has never even dreamed of, and places of terrible beauty and horror pain, and how the Doctor can see so many places and never feel anything always itched at him, until the one day that Nathan realizes that the Doctor does feel, and it's as Nathan is dying (for real, this time, because if anything can kill a immortal energy-elemental that was once human, it's a matter-disrupter) that the Doctor kisses him, and he's never felt so alive and frail. He knows that the Doctor does this to save him; to give him the only kind of energy in the universe like his own, but it doesn't stop Nathan from kissing the Doctor back. It's messy and greedy but so very painfully alive, and Nathan is never more aware of the Doctor then he is right then.
When it stops, as it must stop, Nathan swears he hears the Doctor say something like "that's what you get for messing around with the space-time continuum" before going back to kissing him.