Pablo's feelings about Gris change during the course of his time in the cell, waiting for the soldiers to execute him against the wall. The knowledge that he will inevitably die, however, slowly changes the way he feels about Gris, as well as how he feels about his own life and life in general.
In the beginning, Pablo expresses how he, presumably, might have felt more sympathy for someone like Ramon Gris had he been in the same cell as Pablo, Tom, and Juan. He says,
Fundamentally, I hadn't much sympathy for Tom and I didn't see why, under the pretext of dying together, I should have any more. It would have been different with some others. With Ramon Gris, for example. But I felt alone between Tom and Juan. I liked that better, anyhow: with Ramon I might have been more deeply moved. But I was terribly hard just then and I wanted to stay hard.
At this point, he rationalizes the fact that he doesn't feel much sympathy for Tom not by saying that he can't feel sympathy for people at all, but by saying that he just doesn't care for Tom and Juan the same way he does for Gris.
Later on, however, he completely changes the way he thinks about any person. When he finally decides he has to "die cleanly," he talks about how he must be stubborn and that he cannot let the guards and doctor think he is suffering, and how he cannot cry. Dying cleanly seems to mean he wants to die without emotion and without feeling at all.
As he tries to think about his inevitable death, he realizes, like Tom, that he can't fully grasp the concept. This tension between wanting to know and understand and not being able to know or understand what death will be like drives him to the point of thinking that if death has no meaning, neither does anything else. He says that his beloved doesn't matter, Gris doesn't matter, and his own life doesn't matter. Hanging on to any one of these people or any one memory is completely futile and meaningless in the face of death. The death itself, in Pablo's mind, doesn't mean anything either, because for it to have meaning would mean that it was in some way justifiable or rationalizable. In addition, he has convinced himself that he is already dead, as he cannot feel emotions nor his body. The shooting in the morning, then, would again be futile, because you cannot kill the already dead.
This is all to say that one of the main reasons why Pablo does not (intentionally) turn in Gris is because it simply doesn't matter: it would be Gris's life or Pablo's life, and Pablo's already dead in all ways but corporeally, so why not just kill Pablo? As the story draws to a close, Pablo is playing a game with the officers, telling them lies (or what he believes to be a lie) to make fun of how they ascribe so much meaning and purpose to what Pablo sees now, in his disconnected state, as being completely meaningless and without purpose.
In this story, the figure of Pablo reminds me of Primo Levi's figure of the Musselmann, whom he describes in his memoir/novel about his experiences as a prisoner in a concentration camp during the Holocaust. It's a beautiful book called Survival in Auschwitz that I can only recommend.