While I agree that there are many unsatisfactory loose ends, plotholes and more in Season 3 of Fargo, I don't think Mr. Wrench pursuing Emmit for five years to kill him is one of them. We remember that Nikki believes that Emmit poisoned Sy and killed his own brother Ray, the man she has come to love. She thinks Emmit is the big Villain and later tries to recite the Bible verse before killing him, as she was instructed in the "bowling Alley." So at the end of the scene at the abandoned storage company, when Mr. Wrench asks her if she is happy now that so many are dead, she says that she is not because "the brother", that is Emmit, is still alive. We have seen the growing bond between Mr. Wrench and Nikki, largely because Nikki treats him with respect, has learned ASL to communicate with him and even gives him most of the money! So I find it completely believable that Mr. Wrench would dedicate himself to finishing her mission, that is killing Emmit. Nikki is probably one of the few people who has treated Mr. Wrench well.
What a wonderful conglomeration of shades of truth, misunderstandings, false assumptions and alternative facts Season 3 has been!