As Sam Harris points out, the illusion of free will is itself an illusion. It doesn’t actually feel like you have free will if you look closely enough. So then why are we mistaken about things when we don’t examine them closely enough? Seems like a too-open-ended question.
Is the illusion of the illusion of free will also an illusion? Is it a recursive illusion?
That seems unlikely. There is already a certain difficulty in showing that illusion of free will is an illusion. “It seems like you have free will, but actually, it doesn’t seem.”—The seeming is self-evident, so what sense does it make to say that something actually doesn’t seem if it feels like it seems. As far as I understand it, it’s not like it doesn’t really seem so, but you’re mistaken about it and think that it actually seems so, and then mindfulness meditation clears up that mistake for you and you stop thinking that it seems that you have free will. Instead, you observe that seeming itself just disappears. It stops seeming that you have free will.
So now we come to your suggestion: “It seems(level 2.) like the seeming(lvl 1.) disappears, but actually, it doesn’t seem(lvl 2.) like the seeming(lvl 1.) disappears.”—but once again, the seeming(lvl 2.) is self-evident. So you’d need to come up with some extraordinary circumstances which are associated with more mental clarity to show that that seeming(lvl 2.) also disappears. But this is unlikely, because the concept of free will is already incoherent, so more mental clarity shouldn’t point you towards it.