Learn English – Chasing something that doesn’t exist

I'm trying to find a word or short phrase that would describe chasing something that doesn't exist.

My restriction is that it can't be referencing something that would only make sense in our world (things like "chasing the white whale" as it's a reference to Moby Dick)

I'm writing a book that does not take place on earth. So referencing our literature, specific places on earth, or specific cultures on earth don't really work well with the setting.

I'll be taking a look at worldbuilding.stackexchange.com as well, but for reference for those who comment or come back to view this question.

The world the story takes place in is similar to earth in regards to atmosphere, environments, and natural phenomenon. Things like "chasing the rainbow" would work.

As for context in how I'm trying to use this. Two people are having a tense conversation. Person 1 is attempting to convince Person 2 to join a group that has made person 1 very idealistic promises. Person 2's reply is “You paint a pretty picture, but it’s one drenched in the blood and death of every nation. You use to be so smart, so tactful, now you’re nothing but a fool chasing after a _______________.”