So I'm trying to write a character whose village developed a plague and now he has three months to live. He is now on a quest to find a cure for himself and the people of his village. I do not know how this knowledge would affect his psychology, what I am leaning towards is him becoming more impatient and ruthless to finding his cure which is just out of reach, as the months go by which puts him and his companions in trouble. But I also want a few moments of reflection and to have a slow conversation with him and his companion throughout his adventure, talking about things like : 'If I find a cure we will do this and that etc' Is this approach believable?
That would depend entirely on the character and on what you want him to do. People can have completely different reactions to learning they're dying. For some it's a wake up call, they realize they need to enjoy every moment of life, some will become depressed or desperate. He might take it on entirely as a mission, it's his mission with what life he has left to accomplish what he needs to do. Is he deeply religious or superstitious? Are his people, his tribe? All of this would play a part, and of course you can arrange it all however it works best for the story. All of it falls under the realm of theme. Whatever your overriding theme is, all of these factors should be set up to help get it across.
That he embarks on this quest to find a cure tells me he is not a quitter. He won't let anything stand in his way. Are you going to put an antagonist in his path who hinders him? Then maybe that would be where his 'ruthless' side shows itself. But how sick does this plague make him? How is he still able to undertake this 'adventure'? And yes, scenes of reflection would be very appropriate. Facing death does that to us.
Fearful, terrified possibly. So much so that he, ironically, attempts suicide, but this very irony stops him. It dawns on him, that it is living in fear that is so crippling. There is no alternative, the only antidote, (pun intended) to his dilemma is to discover hope, and the only thing that can offer that, in this situation, is an antidote. There is only one course of action.
