The only two meanings for a twitching tail I know are "I'm hunting" (he's definitely not) or "I'm annoyed". I'm particularly aware of the latter because I once knew a cat whose twitching tail was the only warning you'd get that she'd had enough petting before she'd sink her teeth into you (for some reason she found biting preferable to just getting off of your lap).
My foster's tail-thumping starts up right away as soon as you start giving him attention. He'll be stretched out on his side, purring, and by all appearances enjoying himself... except for the twitching tail. Is he expressing annoyance, or are there other meanings for a twitching tail?