More context is needed for your example. I give you another one. Your father wants you to take your brother back to a distant university. You don't want to do it because it takes too much time and you need to go back to your school. Your mother tells you, if you don't want to do it for your brother or father, do it for my sake (because otherwise there will be a lot tension in the home and I will be forced to live with the anger of others)

Jo must be a person in the story. It means "for Jo's sake if not [for] your own [sake]." When you are asked to do (or not do) something "for somebody's sake" it means that you are being asked to do (or not do) that thing so that the named person will not be upset, harmed, angry, or affected by the consequences. It means "please let me be your brother, because it will benefit Jo in some way if you let me. I know you might not want to do it to benefit yourself, because perhaps you do not care about seeking your own benefit, but please think about how it will benefit Jo". Some common expressions in English are: "For God's sake" (but this is considered blasphemous by some religious people) "For Goodness' sake" (this is considered an acceptable alternative to the above) "For Pete's sake" (I do not know why we use the name Pete. We just do) "For pity's sake" (this means "have pity on me and please stop what you are doing!") All of these expressions I have listed are used to express negative emotions such as anger, frustration, and impatience. However, in the case of saying "for Jo's sake" in the novel, the speaker is probably not angry. They are just being earnest and making an appeal on behalf of the character called Jo.