  We show that Toda shock waves are asymptotically close to a modulated finite
gap solution in the region separating the soliton and the elliptic wave
regions. We previously derived formulas for the leading terms of the asymptotic
expansion of these shock waves in all principal regions and conjectured that in
the modulation region the next term is of order $O(t^{-1})$. In the present
paper we prove this fact and investigate how resonances and eigenvalues
influence the leading asymptotic behaviour. Our main contribution is the
solution of the local parametrix Riemann-Hilbert problems and a rigorous
justification of the analysis. In particular, this involves the construction of
a proper singular matrix model solution.
