"How Can I Miss You When You Won't Go Away," circa 1972, is by Dan Hicks and the Hot Licks, a great California outfit specializing in humorous tunes played (with dead seriousness and consummate skill) in a Western Swing style. I'm pretty sure the instrumentation was all-acoustic, with a very hot fiddle prominently featured.

*All* of Dan's songs were/are hilarious, but I can't think of a title any better than this one.