Klingler's Shimura-type conjecture for variations of Hodge structures

Let ${\mathbb V}$ be a ${\mathbb Z}$-variation of Hodge structure on a smooth irreducible complex quasi-projective variety $S$. A point of $S$ is a CM point for $(S,{\mathbb V})$, and $(S,{\mathbb V})$ is of Shimura type when it arises from a Shimura datum in the sense of the source. Klingler's conjecture. If the set of CM points for $(S,{\mathbb V})$ is Zariski-dense in $S$, then $(S,{\mathbb V})$ is of Shimura type. This is the non-classical geometric component isolated from Klingler's broader characterization conjecture; the source gives no resolution status.