Karl Fogel at
Why we will always need the hyphen, exhibit 3.14x10e35:
"So then I went off on this wild goose chase..."
Which is wild, the goose or the chase? Could go either way.
Having received implied doubts from some quarters, I'd like to be clear about something:
I have, in fact, chased a wild goose before, and the chasing process was itself wild because the goose was wild. So in my, um, lived experience, the linguistic ambiguity remains.