Flanders & Swann also had an elephant song, about an elephant who malingered amnesia:

I'm suffering from amnesia.
Me mind's a perfect blank.
Now life is very much easier:
Amnesia's to thank.

He went on to develop other symptoms:

I suffer from schizophrenia.
It comes on me in spells.
Sometimes I'm King of Armenia,
And others I'm Orson Welles.
I've told my psychoanalyst
That I'm a sacred cow.
I'd like to carry a howdah, but
I can't remember how.