  Let $A$ be a finite subset of $L^2(\mathbb{R})$ and $p,q\in\mathbb{N}$. We
characterize the Schauder basis properties in $L^2(\mathbb{R})$ of the Gabor
system $$G(1,p/q,A)=\{e^{2\pi i m x}g(x-np/q) : m,n\in \mathbb{Z}, g\in A\},$$
with a specific ordering on $\mathbb{Z}\times \mathbb{Z}\times A$. The
characterization is given in terms of a Muckenhoupt matrix $A_2$ condition on
an associated Zibulski-Zeevi type matrix.
