  We study a version of the fractal uncertainty principle in the joint
time-frequency representation. Namely, we consider Daubechies' localization
operator projecting onto spherically symmetric $n$-iterate Cantor sets with an
arbitrary base $M>1$ and alphabet $\mathscr{A}$. We derive an upper bound
asymptote up to a multiplicative constant for the operator norm in terms of the
base $M$ and alphabet size $|\mathscr{A}|$ of the Cantor set. For any fixed
base and alphabet size, we show that there are Cantor sets such that the
asymptote is optimal. In particular, the asymptote is precise for the mid-third
Cantor set, which was studied in part I. Nonetheless, this does not extend to
every Cantor set as we provide examples where the optimal asymptote is not
achieved.
