  In this paper, we describe a certain kind of $q$-connections on a projective
line, namely $Z$-twisted $(G,q)$-opers with regular singularities using the
language of generalized minors. In part one arXiv:2002.07344 we explored the
correspondence between these $q$-connections and $QQ$-systems/Bethe Ansatz
equations. Here we associate to a $Z$-twisted $(G,q)$-oper a class of
meromorphic sections of a $G$-bundle, satisfying certain difference equations,
which we refer to as generalized $q$-Wronskians. Among other things, we show
that the $QQ$-systems and their extensions emerge as the relations between
generalized minors, thereby putting the Bethe Ansatz equations in the framework
of cluster mutations known in the theory of double Bruhat cells.
