Waiting for Godot without Godot is a rare phrase that always occurs in association with Hamlet without the Prince, on which it was probably modelled.

The latter phrase, first recorded in 1810, refers to The Tragedy of Hamlet, Prince of Denmark, by the English playwright and poet William Shakespeare (1564-1616).—Cf. ‘Hamlet without the Prince’: meaning and origin.

The former phrase refers to Waiting for Godot, a play by the Irish author Samuel Beckett (1906-1989). (This play, which premiered in London in 1955, is Samuel Beckett’s translation of his own original French-language play, En attendant Godot, which premiered in Paris in 1953.)

Although these two phrases always occur in association with each other, the difference between Waiting for Godot without Godot and Hamlet without the Prince is that the latter phrase is based on the absurdity of performing, without an actor playing the title role, The Tragedy of Hamlet, Prince of Denmark, whereas the former phrase is, in itself, absurd, since the titular character never appears in Waiting for Godot.

—Cf. also ‘Lear without the King’ | ‘Henry V without the King’.

The only occurrences of the phrase Waiting for Godot without Godot that I have found are as follows, in chronological order:

1-: From Sketch: A Christmas without Santa missing, by the British journalist Simon Hoggart (1946-2014), published in The Guardian (London and Manchester, England) of Friday 17^th December 1999:

Treasury questions yesterday, and no sign of Gordon Brown *. Questions without Gordon is empty—like Hamlet without the prince, Henry V without the king, or Waiting For Godot without Godot. Well, not the last perhaps, but you get the idea.

[* The British Labour statesman Gordon Brown (born 1951) was then the Chancellor of the Exchequer in the government of Tony Blair.]

2-: From Concrete or Abstract Conceptions of Discrimination?, by George Rutherglen, in Philosophical Foundations of Discrimination Law (Oxford University Press, 2013), edited by Deborah Hellman and Sophia Moreau:

Are prohibitions against discrimination impossible without the concept of discrimination, like “Hamlet” without the Prince? Or are they entirely conceivable like “Waiting for Godot” without Godot?

3-: From Real Tigers (London: John Murray, 2016), by the British novelist Mick Herron (born 1963):

Lamb killed his cigarette end in yesterday’s half-full teacup.
‘Besides,’ he said. ‘It’s not like her to disappear.’
‘“Disappear” is a bit strong,’ said Shirley.
‘Really? What would you call it?’
‘… Not being here?’
‘And what would happen if we all did that? What would it be like if I was just not here all of a sudden?’
Shirley seemed about to speak, but changed her mind.
‘It would be like Hamlet without the Prince,’ River suggested.
‘Precisely,’ Lamb said. ‘Or Waiting for Godot without Godot.’
Nobody touched that one.