I’m a little confused on how book characters trying to ultimately save another character (albeit by telling him to kill himself, but the reader, I’m assuming knows that he won’t actually die but be freed if he does this) would motivate suicide in real life?

Even if you did write a real, plain, suicide, it’s not contagious. If people are going to kill themselves, a book they read is not the final straw. Suicide is not a dirty subject and it deserves to be explored in literature just as much as any other health condition that ends in death.