Whilst doing research for my 3D nesting project, I popped onto the online OED database and looked up "rat."
Here are a couple of the definitions that I found:

g. to get (or have) a rat (or rats): to be eccentric or insane. Austral. and N.Z. slang. [1890 Barrere & Leland Dict. Slang II. (American), 'to have rats', to have wild or eccentric fancies.]

ADDITIONS SERIES 1997
rat, n
e. rat-arsed a. slang, drunk, tipsy