  In the first article of this work [... I: The transposition map] we showed
that real Clifford algebras CL(V,Q) posses a unique transposition
anti-involution \tp. There it was shown that the map reduces to reversion
(resp. conjugation) for any Euclidean (resp. anti-Euclidean) signature. When
applied to a general element of the algebra, it results in transposition of the
associated matrix of that element in the left regular representation of the
algebra. In this paper we show that, depending on the value of (p-q) mod 8,
where \ve=(p,q) is the signature of Q, the anti-involution gives rise to
transposition, Hermitian complex, and Hermitian quaternionic conjugation of
representation matrices in spinor representations. We realize spinors in
minimal left ideals S=CL_{p,q}f generated by a primitive idempotent f. The map
\tp allows us to define a dual spinor space S^\ast, and a new spinor norm on S,
which is different, in general, from two spinor norms known to exist. We study
a transitive action of generalized Salingaros' multiplicative vee groups
G_{p,q} on complete sets of mutually annihilating primitive idempotents. Using
the normal stabilizer subgroup G_{p,q}(f) we construct left transversals,
spinor bases, and maps between spinor spaces for different orthogonal
idempotents f_i summing up to 1. We classify the stabilizer groups according to
the signature in simple and semisimple cases.
