I think what happens is you squat normally until you need to take a few breaths between reps.
eg, you do 8 reps taking a breath between each reps you take a couple of breaths before rep 9 do a couple more reps with one breath between reps, then rep 12 you may need to take 2 -3 breaths before you can attempt rep 13, then after rep 13 you will probably need a few breaths before each rep is attempted,
So basically sometime in the set the set goes from doing normal reps to doing rest pause reps.
I remember in my HIT days when I was a scrawny little weakling I would do 12-20 reps on the leg extension then move instantly without rest onto squats.
I would only be able to get to rep 8 or 9 (something like that) before I had to quit and it wasn't muscular failure that made me quit it was lack of air that made me quit.