We provide the missing member of a family of four $q$-series identities related to the modulus 36, the other members having been found by Ramanujan and Slater. We examine combinatorial implications of the identities in this family, and of some of the identities we considered in "Identities of the Ramanujan-Slater type related to the moduli 18 and 24," [\emph{J. Math. Anal. Appl.} \textbf{344}/2 (2008) 765--777].