The $K_6$ minor conjecture for triangles and induced $K_{3,3}$ minors

Let $G$ be a graph. A minor of $G$ is obtained by deleting vertices and edges and contracting edges; an induced minor is obtained by deleting vertices and edges and contracting connected vertex sets. A triangle is a cycle of length three.

$K_6$ minor conjecture. If $G$ contains $K_6$ as a minor, then $G$ contains a triangle as a subgraph or $G$ contains $K_{3,3}$ as an induced minor.

This proposes a structural consequence of having a $K_6$ minor, separating the presence of a triangle from the induced-minor obstruction $K_{3,3}$. The source presents it as an open proposal and gives no resolution.