Why is it that when I want my cat to sit on my lap (humans need companionship too), he not only declines but ignores me? But if I'm reading a book or watching TV, THAT'S when he decides to be companionable and sit on my lap - blocking said book or TV.

This is very simple. Your cat is trying to make sure you understand the natural order of things. Just because you want a warm lap, that doesn't mean you're entitled to one. But, when you have a book, or are watching TV, or have your computer on your lap, the cat must sit on you, because you need to be reminded what happens to be the most important thing in the house, and that would be the cat. There is no point in getting upset over this. If you want the cat in your lap, just pick a book up, and then you both win.