Disconnectedness conjecture for the Hénon connectedness locus

Let $f_{c,b}(x,y)=(x^2+c-by,x)$ be the complex Hénon family, with $(c,b)\in\mathbb{C}^2$, and let $\mathcal{M}$ be the set of parameters for which the Julia set $J_{c,b}$ is connected.

Disconnectedness conjecture. The connectedness locus is disconnected:

$$\mathcal{M}\text{ is disconnected.}$$

This is a parameter-space question for Hénon maps and is presented as an open problem in the paper.