  In this paper, we revisit an earlier conjecture by one of us that related
conjugacy classes of $M_{12}$ to Jacobi forms of weight one and index zero. We
construct Jacobi forms for all conjugacy classes of $M_{12}$ that are
consistent with constraints from group theory as well as modularity. However,
we obtain 1427 solutions that satisfy these constraints (to the order that we
checked) and are unable to provide a unique Jacobi form. Nevertheless, as a
consequence, we are able to provide a group theoretic proof of the evenness of
the coefficients of all EOT Jacobi forms associated with conjugacy classes of
$M_{12}:2 \subset M_{24}$. We show that there exists no solution where the
Jacobi forms (for order 4/8 elements of $M_{12}$) transform with phases under
the appropriate level. In the absence of a moonshine for $M_{12}$, we show that
there exist moonshines for two distinct $L_2(11)$ sub-groups of the $M_{12}$.
We construct Siegel modular forms for all $L_2(11)$ conjugacy classes and show
that each of them arises as the denominator formula for a distinct
Borcherds-Kac-Moody Lie superalgebra.
