Pink chit
The gnarled ancients of my father's (early post-war National Service) generation told me years ago that the term comes from the colour of the chit you had to get indicating that you had permission to be off base.
That's the explanation I give to bemused junior colleagues - I got so used to hearing it from adults when growing up, I'm still using it.
Hope it isn't really a reference to some form of medical certificate.....