Let $X\subset\mathbb{P}^4$ be an hypersurface of degree six given by the Pfaffian of a $6\times 6$ matrix $M$ whose entries are quadratic forms in the homogeneous coordinates of $\mathbb{P}^4$. I am interested in the singular locus of $X$.

Is it true that $Sing(X)$ is the curve defined by the $4\times 4$ sub-Pfaffians of $M$?

In this case, is it known that $X$ has ordinary singularities along $Sing(X)$, and what is the multiplicity of $Sing(X)$ for $X$?

What about the same questions for the following $$ \left( \begin{array}{cccccc} 0 & x_1^2 & x_2^2 & x_3^2 & x_4^2 & x_5^2\\ -x_1^{2} & 0 & x_1x_3 & x_2x_4 & x_3x_5 & -x_4x_5\\ -x_2^{2} & -x_1x_3 & 0 & x_1x_5 & -x_2x_5 & -x_3x_4\\ -x_3^{2} & -x_2x_4 & -x_1x_5 & 0 & -x_1x_4 & -x_2x_3\\ -x_4^{2} & -x_3x_5 & x_2x_5 & x_1x_4 & 0 & -x_1x_2\\ -x_5^{2} & x_4x_5 & x_3x_4 & x_2x_3 & x_1x_2 & 0 \end{array} \right) $$ particular Pfaffian?