Good question. It took me a while to get this myself. I agree focusing on the glove side is not intuitively obvious. But, just "trying to stay closed" is gonna be difficult if you've got something else going on that competes with your ability to stay closed. A glove-side tilt makes it difficult to separate hips and shoulders. Try it. Stand up and lean to your glove side and then try to rotate the hips as far as they'll go while keeping the shoulders closed. It's much more difficult than if you maintain good posture. Getting good separation requires good timing as well. Flying out with the glove tends to destroy timing by pulling the shoulders open early. Getting good separation means delaying shoulder rotation long enough for the hips to fully rotate first. It really is a timing thing.
That book has some things in it that are still valid but it's not his latest. The Art and Science of Pitching is his latest book that describes his mechanics model. Fastball Fitness describes training protocols but also has an excellent section that describes how each part of the body contributes to velocity. His latest book is called Arm Action, Arm Path, and The Perfect Pitch: Building the Million Dollar Arm. It attempts to use science to debunk a lot of the common traditional wisdom teaches we hear a lot. I originally thought this latest book would be optional reading but I'm just about finished reading it and I think it should be required reading for pitchers. If you can afford it (none of these books are very expensive), I would recommend getting all three of them.
Ok, so it takes good timing to maximize one's separation. How much separation one is able to get is dependent on their flexibility and will differ from pitcher to pitcher. But it also takes some neuromuscular patterning. In other words, you've got to be "wired" to do it. For many young pitchers, this is a real hurdle. For not as young pitchers, it still might be somewhat foreign. In these cases, getting it figured out is the first step. The drills I mentioned put your body into positions and movements where you can start to feel what separation feels like. Once you've got the parts working, then you can start to work on optimizing them.
So, I've given you some up-front stuff in the form of drills and some timing stuff that starts with the glove side. If you do things well - good posture and balance, good momentum, good timing starting with good glove side management, etc. - hip and shoulder rotation should take care of themselves.