Similar to the Irish Goodbye, but derives from a sense of paranoia and feeling uncomfortable in the current environment rather than being too drunk.
"I couldn't handle when your Dad came outside and talked to us. I had no choice but to Jamaican Farewell."
Cheech: "What happened to you last night Chong?"
Chong: "Man, I had to pull a Jamaican Farewell man. That weed got me too stoned."