I just did this tour last Saturday. They just take 20 people per group. I tried some mock bookings and even at 8 a.m. EST 60 days in advance it was full for every time slot. I booked at 5:00 a.m. EST 60 days in advance and was able to get two tickets. As others have said which I didn't realize when I booked, you can book after midnight.
If the tours are full they don't show up online. I wanted to book the 9:30 a.m., but that didn't show up, but I was able to get the 9:00 a.m. when I did my booking and 8 and 8:30 a.m. were still available too. I did though notice a group that was doing the 9:30 a.m. so I know it wasn't that they weren't doing that time slot that day.
If offsite you can only book 60 days in advance. I believe hotel guests can book 60 days before their stay, so if not doing it day 1 can book more than 60 days in advance. Call Disney if you have further questions and they can let you know if you are too early or too late.
Oh and FYI -- my thoughts about the tour. I enjoyed it, but the utilidors really just seemed like a larger version of the ground floor of a cruise ship. Honestly I found the last behind the scenes tour I did on one of the big
Royal Caribbean cruise ship more interesting than this tour -- the cruise version of the utilidors was more active and more interesting to me and I saw the galleys (so impressive how they feed so many so well), bridge and navigation equipment, engine room, laundry areas, employee cabin and relaxation areas, all kinds of things, etc. I did, though, learn new Disney facts and trivia and wasn't bored at all. While I think it was a good tour and enjoyable, given the hefty price tag of the tour plus an MK ticket and the fact that other family members have done behind the scenes cruise tours, I'm not recommending it to them. It was on my bucket list for the last 17 year, so I was super curious and happy to finally do it.