"Question: Would one class ignorance in the same category as false knowledge? Does Nietzsche class these in the same category?"
Ones could say ignorance is not the same as false knowledge because ignorance relates to non-existence and false knowledge relates to existence of something false. A decision based on ignorance, excluding disinformation, would be more accurate than a decision based on disinformation, because disinformation misleads. Nietzsche wrote about "ignorance":
“The will to truth, which is still going to tempt us to many a hazardous enterprise; that celebrated veracity of which all philosophers have hitherto spoken with reverence: what questions this will to truth has already set before us! What strange, wicked, questionable questions! It is already a long story – yet does it not seem as if it has only just begun? Is it any wonder we should at last grow distrustful, lose our patience, turn impatiently away? That this sphinx should teach us too to ask questions? Who really is it that here questions us? What really is it in us that wants 'the truth'? - We did indeed pause for a long time before the question of the origin of this will – until finally we came to a complete halt before an even more fundamental question. We asked after the value of this will. Granted we wanted truth: why not rather untruth? And uncertainty? Even ignorance? - The problem of the value of truth stepped before us – or was it we who stepped before this problem? Which of us is Oedipus here? Which of us sphinx? It is it seems, a rendezvous of questions and question-marks. - And, would you believe it, it has finally almost come to seem to us that this problem has never before been posed – that we have been the first to see it, to fix our eye on it, to hazard it? For there is a hazard in it and perhaps there exists no greater hazard." (Nietzsche 2003: 33)
“O sancta simplicitas! What strange simplifications and falsification mankind lives in! One can never cease to marvel once one has acquired eyes for this marvel! How we have made everything around us bright and free and easy and simple! How we have known how to bestow on our senses a passport to everything superficial, on our thoughts a divine desire for wanton gambolling and false conclusions! - how we have from the very beginning understood how to retain our ignorance so as to enjoy an almost inconceivable freedom, frivolity, impetuosity, bravery, cheerfulness of life, so as to enjoy life! And only on this now firm and granite basis of ignorance has knowledge hitherto been able to rise up, the will to knowledge on the basis of a far more powerful will, the will to nonknowledge, to the uncertain, to the untrue! Not as its antithesis but – as its refinement! For even if, here as elsewhere, language cannot get over its coarseness and continues to speak of antithesis where there are only degrees and many subtleties of gradation; even if likewise the incarnate tartuffery of morals which is now part of our invincible 'flesh and blood' twists the words in the mouths even of us men of knowledge: here and there we grasp that fact and laugh at how it is precisely the best knowledge that wants most to hold us in this simplified, altogether artificial, fabricated, falsified world, how willy-nilly in love with error because, as a living being, it is – in love with life!" (Nietzsche 2003: 55)
"Question: Are there any compelling arguments for the will to untruth? In this question I have assumed untruth to mean false knowledge, not ignorance."
There are arguments for the will to untruth, especially favoring groups only or individuals only, relating to profits and survival.
"Question: To the readers of this question, what are your thoughts?"
Thoughts about God are decisive when considering Truth, the idea, which causes honesty. Caiaphas syndrome is relevant. The idea Love, which caused social contract theory and the law is a balancing idea with regard to Truth. Only Truth or only Love can lead to despotism, therefore it is preferable to balance the ideas with the other. Dialectic inclinations and reductionist philosophy to identify essence make many people choose either only Truth or only Love, which leads to problems. Only Truth leads to problems for individuals, due to Caiaphas syndrome. Only Love leads to problems regarding sustainability, due to lacking creativity.
"And do you believe that we humans brought this issue to the surface, or was it fate?"
I do not know where it originated. Animals use deceit and true warnings, therefore it is not only humans, who use the two methodologies, for survival.
NIETZSCHE, F. 2003. Beyond Good and Evil, Prelude to a Philosophy of the Future. London: Penguin, 3rd edition.