Disclaimer: I don't own Doctor Who or anything related to it.
He waits. Not out of fairness to her; not a bit of this is fair to her. He waits because he doesn't think he would be able to handle it if he didn't. A few decades, a few centuries, once he went an entire regeneration. It still wasn't enough. Not enough to be able to properly distinguish them in his hearts. Not enough to see her as she was instead of seeing the ghost he is chasing. But long enough that the longing outweighed the fresh pain he saw upon looking at her. And the guilt.
Clara, his Clara, the real Clara, would never have let him get away with it. I'm not a bargain basement stand-in for somebody else. I'm not going to compete with a ghost. But the echoes are different, born as they were from her love for him, born with a need to help him. It hurts them, each of them, he can tell. But it isn't enough to drive them away. I was born to save the Doctor.
He does come to care for each of them individually in time. They are all different enough for that. It's a terrible cycle. Mourn. Find her. Project love for Clara onto her. Love her for real. Lose her. Repeat. Even when he comes to love each echo for herself though, he misses Clara.
He needs to stop, he thinks, as he stand over yet another grave. Another Oswin this time. 51st century. Survived her original run in with him rather easily from what she had told him. Minimal trauma. She had been happy. That was rare. Being born to save him was a hazardous and painful destiny it seemed. Many didn't survive at all. But among the thousands and thousands of her throughout time and space, it was inevitable that some would survive, even thrive occasionally. Still it wasn't like they were infinite. Eventually he would stop. One way or another. Of his own will or standing over the grave of the very last Clara Oswald in the universe.
It would be better to stop here, he thinks. He and Oswin had a marvelous time. He got to spend many long decades with her, not long by his standards maybe, but the majority of her life. And happy decades at that. Yes, better to stop here. End on a high note.
But he's fooling himself. He's just waiting. As usual. Maybe a little longer than usual, but he was always going to look again. Because whatever he thinks about high notes and endings, his next face, well, she doesn't quite agree.
'This was always going to happen.' she thinks, half resigned, half filled with self mockery. 'Spend a few millennia obsessed with the same woman and well...' her thoughts trail off as she stares into the far too familiar brown eyes in the mirror.
And suddenly the urge to find her again is stronger than it's ever been. She wonders with some amusement whether that might be some of Clara's egomania coming out in her own personality. Because oh yes, it couldn't just be Clara's face she took on, no it had to be bits of her personality as well. Well, her distorted subconscious view of Clara anyway. She doubts the overwhelming urge she has to make a souffle right now is how the real Clara ever felt about it.
It takes a while to find something in the wardrobe in her size that neither Clara nor one of her echoes ever wore. She doesn't think she could handle wearing Clara's clothes.
When she returns to the console room, which now resembles the living room of Clara's flat to a disturbing degree, she moves to the console and begins entering coordinates before she even realizes what she's doing. Her last face had found her long ago of course. He could bring himself to stay away, but he couldn't stop himself from looking. And as she sets the TARDIS into flight she realizes there was never a question with this face. She was going to go to her from the moment she regenerated.
'The hard way it is, I guess.' she thinks with a sigh. Because she's realized she is never going to stop chasing Clara Oswald as long as she has a choice.