"pursuit of anything in ignorance of the direction it will take," hence "a foolish enterprise," 1592, first attested in "Romeo and Juliet," where it evidently is a figurative use of an earlier (but unrecorded) literal sense in reference to a kind of follow-the-leader steeplechase, perhaps from one of the "crazy, silly" senses in goose (n.). Wild goose (as opposed to a domesticated one) is attested in late Old English (wilde gos).
c. 1600, "wild, undomesticated," from French feral "wild," from Latin fera, in phrase fera bestia "wild animal," from ferus "wild" (from PIE root *ghwer- "wild beast"). Since 19c. commonly "run wild, having escaped from domestication."