This argument needs some reason tbh.
I've never read a book specific to this topic but if you want one, here's one that looks good, engineer-friendly and simple enough: https://mitpress.mit.edu/books/outer-limits-reason
But as far as I know there's no proof that consciousness is beyond the limits of reason. The mere fact that reason is limited is not a universal argument against all rational discussion.
I'm not really that much in the debate about consciousness but I'm a lot into the one about intelligence: there are many definitions of intelligence and none of them seems satisfying. You can define intelligence from a rational point of view, as some kind of function or model, but it's extremely narrow, arbitrary and limited. That's the trick he uses. To me it's not enough. The very idea of intelligence is restrictive, antropocentric and confusing. That's because with the existing tools we have (including reason) we cannot converge to a satisfying idea of intelligence, that eludes our analysis.