Was Gaudapada an idealist as many scholars have asserted? Without going into the knotty questions as to what sort of idealism it was that he might or might not have been; I think it more fruitful to ask - what did Gaudapada aim at in his inquiry.
Let’s have a cup of chai and focus on this. In his own way he was a strict eliminativist. What is it that’s left and cannot be denied if one ignores the differences between the various modes of consciousness?What but consciousness itself which is never not ‘on’ even in Deep Dreamless Sleep (sushipti). The latter observation is very important in the thought of Sankara. Gaudapada threw all states and modes of consciousness into the pot and distilled their essence to find the unchanging, unborn, pure, consciousness. This and not a quasi method of doubt is the source of such verses as IV. 41: (Karikas)
As some one, owing to lack of discrimination, may, in the waking state, be in contact with unthinkable objects, fancying them to be real, so also in dream, one sees the objects in that dream alone, owing to lack of discrimination.
To say that Gaudapada was an ‘illusionist’ is to escape the gravamen of his case against trying to find ultimate reality within the data of awareness. He never leaves off his ontologically eliminativist cap but can recognise that there are grades of realisation:
Instruction about creation has been imparted by the wise for the sake of those who , from the facts of experience and adequate behaviour, vouch for the existence of substantiality, and who are ever afraid of the birthless entity.
Sankara in his commentary adds to his observation that:
That creation has been preached as a means to an end (for generating firm discrimination) under the idea: “Let them accept it for the time being. But in the course of practising Vedanta, the discriminating knowledge about the birthless and non-dual Self will arise in them spontaneously."
So it looks like Idealism, talks like Idealism but doesn’t walk like Idealism. The world is a given yes, but a given open to ontological question.