The Man should have a TN/TX accent. Not a twang. Like Josh Brolin in No Country. He is gruff and suspicious, albeit somewhat of a Samaritan, as he stops to help someone when he has no reason to. His motives are unclear.

The Woman does not need an accent, but a slight TN influence could show through, showing she has not been there as long as the Man. She is highly suspicious of the Man and his motives, but hers are questionable as well. She tells the Man she is running from something, but she is not weak, her lines are direct and meant to pack a punch, and she is quicker to it than he.