At http://uk.answers.yahoo.com/question/index?qid=20130121094111AAKfmOb is an explanation of the usage of the expression 'Box and Cox' that comes close to how I remember it being used some 40 years ago here in the North of England. Also its origin. I've tidied it slightly - apologies to Bilbo:
[This expression refers] to a mid-19th century farce about two men
(Cox and Box) who occupied the same lodgings, one by day the other by
night - the original play was by John Maddison Morton, and Arthur
Sullivan made a highly successful operetta out of it. It is now a
rather quaint way of describing any pair taking alternate turns at
I remember that the ludicrousness of the situation (the brothers are unaware that they share the lodgings for most of the farce - that being why it's a farce) was an important factor in the wider use of the expression. So, the improbable alternate missing of contacts fits well here. The expression was never, to my knowledge, used for prosaic turn-taking.
Though there are plenty of Google hits, the expression does seem to have fallen out of favour in recent years. Perhaps the second part of the above quote provides the answer, though I'd guess it's merely that the expression now sounds dated and uncool.
As both words have a rather lewd slang interpretations (rather
appositely alternate terms for male and female gentialia) it tends to
have fallen into disuse as it then does not convey the same sense as
A disambiguation from Wikipedia:
Cox and Box, or The Long-Lost Brothers, is a one-act comic opera with a libretto by F. C. Burnand and music by Arthur Sullivan, based
on the 1847 farce
Box and Cox
by John Maddison Morton.
Probably both variants have been used in the wider sense.