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We continue our study of the density of the odd values of eta-quotients, herefocusing on the $m$-regular partition functions $b_m$ for $m$ even. Based onextensive computational evidence, we propose an elegant conjecture which, inparticular, completely classifies such densities: Let $m = 2^j m_0$ with $m_0$odd. If $2^j < m_0$, then the odd density of $b_m$ is $1/2$; moreover, suchdensity is equal to $1/2$ on every (nonconstant) subprogression $An+B$. If $2^j> m_0$, then $b_m$, which is already known to have density zero, is identicallyeven on infinitely many non-nested subprogressions. This and all otherconjectures of this paper are consistent with our ''master conjecture'' oneta-quotients presented in the previous work.  In general, our results on $b_m$ for $m$ even determine behaviorsconsiderably different from the case of $m$ odd. Also interesting, itfrequently happens that on subprogressions $An+B$, $b_m$ matches the parity ofthe multipartition functions $p_t$, for certain values of $t$. We make asuitable use of Ramanujan-Kolberg identities to deduce a large class of suchresults; as an example, $b_{28}(49n+12) \equiv p_3(7n+2) \pmod{2}$. Additionalconsequences are several ''almost always congruences'' for various $b_m$, aswell as new parity results specifically for $b_{11}$.  We wrap up our work with a much simpler proof of the main result of a recentpaper by Cherubini-Mercuri, which fully characterized the parity of $b_8$.

Parity of the coefficients of certain eta-quotients, II: The case of even-regular partitions