  It was proved in 2010 that the principal Kac--Wakimoto hierarchy of type $D$
is a reduction of the 2-component BKP hierarchy. On the other hand, it is known
that the total descendant potential of a singularity of type $D$ is a
tau-function of the principal Kac--Wakimoto hierarchy. We find explicitly the
point in the Grassmanian of the 2-component BKP hierarchy (in the sense of
Shiota) that corresponds to the total descendant potential. We also prove that
the space of tau-functions of Gaussian type is parametrized by the base of the
miniversal unfolding of the simple singularity of type $D$.
