Abbreviation of the phrase 'Wild Juice Case'. Which is a drunken mispronunciation of the phrase 'Wild Goose Chase'.
The term was originally coined as a drunken slur used to describe a car journey home from the pub which according to an inebriated passenger included unnecessary detours.
The term is now used to describe any pre-longed car journey after a drinking session where the driver and/or other passengers are sober so that they can continue to be entertained by members of the group who are intoxicated after having left the pub.
“Lets go on a wild juice case!” (Meaning: “Lets go on a wild goose case!”)