Conjecture on the components of the rank-two locus of the cubic discriminant

Let $V_k$ be the locus of cubic surfaces for which the matrix $M$ has rank at most $20-k$, and let $N_2$ denote the locus of binodal cubic surfaces. The $19\times 19$ minors of $M$ define $V_2$. Conjecture on $V_2$. The locus $V_2$ has at least two irreducible components parameterising binodal and cuspidal cubic surfaces. In particular,

$$N_2\subset V_2$$

and the $19\times 19$ minors of $M$ vanish on $N_2$. This is suggested by the computation that a general plane section of $V_2$ consists of $400$ points, matching the $280$ binodal and $120$ cuspidal cubic surfaces in the singular locus of the discriminant curve; the claim remains conjectural, although the binodal inclusion is verified in a normal-form computation.