  In the previous paper [Sun23], the author proved a uniform bound for sums of
half-integral weight Kloosterman sums. This bound was applied to prove an exact
formula for partitions of rank modulo 3. That uniform estimate provides a more
precise bound for a certain class of multipliers compared to the 1983 result by
Goldfeld and Sarnak and generalizes the 2009 result from Sarnak and Tsimerman
to the half-integral weight case. However, the author only considered the case
when the parameters satisfied $\tilde m\tilde n<0$. In this paper, we prove the
same uniform bound when $\tilde m\tilde n>0$ for further applications.
