As a visual metaphor, it implies the opposite to the expression ‘flat out’. A lizard drinking is visually flat against the ground, still, stationary, prostrate, prone and apparently inactive - the opposite of what a person is like when they are busy.
The primary definition that I heard for years amongst colleagues and friends fluent in Strine was the 'not busy' version. It was only recently that I have heard it used to mean 'hard at work' or 'busy'. It feels that the traditional components of visual metaphor and humour in the Strine lexicon have been lost or the expression misconstrued at some point.