  In [4] and [5], Folsom presents a family of modular units as higher-level
analogues of the Rogers-Ramanujan $q$-continued fraction. These units are
constructed from analytic solutions to the higher-order $q$-recurrence
equations of Selberg. Here, we consider another family of modular units, which
are quotients of Hall-Littlewood $q$-series that appear in the generalized
Rogers-Ramanujan type identities of [6]. In analogy with the results of Folsom,
we provide a formula for the rank of the subgroup these units generate and show
that their specializations at the cusp $0$ generate a subgroup of the
cyclotomic unit group of the same rank. In addition, we prove that their
singular values generate the same class fields as those of Folsom's units.
