Isn’t / Isn’t there / Aren’t looks a good hint for Nach eil while Don’t / Aren’t / Isn’t like a hint for just Nach – since nach is just the negative questioning particle (and can mean just don’t in don’t you run every day? question as well as isn’t in isn’t it a language course?) and nach eil is the particle with the verb tha, meaning always isn’t in cases like isn’t it beautiful?, isn’t the cat on the table?, don’t we have wine? – lit. isn’t wine at us?.
But anyway, the hints are just this – hints showing you roughly the meaning of single words or phrases, which might not translate exactly in context (like here, even though nach eil means isn’t?, English translation doesn’t have it, since it uses a different verb entirely; to have rather than to be at).