Another Scottish writer and mystery novelist is Ian Rankin. In place of the word short he uses shy, but the expressiveness is the same.

one/a couple of X shy of a Y = "not all there"

"Rebus was beginning to suspect that the secretary was a couple of keys short of a typewriter." (Ian Rankin, Tooth and Nail, 1992)

"Sounds to me like he's one domino shy of a set." (Id., Strip Jack, 1992)

"Cafferty turned to stare at Hynds, as if offering him the chance to concur that Rebus was a couple of waltzers shy of a fairground." (Id., Resurrection Men, 2001)