My understanding (as I own all three books) is that the third book introduces the crab -what makes book 2's thumb position unique? I just found it and was looking through it and I did not see any references to pivots or the crab technique.
It's not possible to "pivot" in thumb position, if we're using the term properly. The crab technique is an alternative to shifting, but is yet another approach. In crab, one opens and closes their hand while any given finger works as an "anchor" to push or pull their hand into the new position. Rabbath may not have invented the concept (although he seems to have derived it independently), but he has written extensive studies for it.
What makes volume two's thumb position material unique? Very little, considering almost none of the book is in thumb position (although most of the etudes can be played in any position, as you will see in volume four). Just about the only part of the book in thumb position, page 33, is a study in hand shapes and full hand extension (rather than individual finger extensions).
To me, some of the defining characteristics of Rabbath's left hand technique in regards to thumb position include:
- Use of the six position system, based on the harmonic nodes of the string.
- Use of all four strings in all six positions, which facilitates much faster playing.
- Use of the full weight of his arm. He leans the bass back and allows gravity to pull the weight of his arm through his fingers and into the string and fingerboard.
- Hand shapes. Check out the pictures in the supplemental packets that comes with each volume.
- Crab technique, which I've already described.
- Use of "thumb position" in lower registers.