The NP-hardness conjecture for lower oriented general position number two

Let $G$ be a graph, and let ${\rm gp}_{\rightarrow}(G)$ denote the minimum general position number over all orientations of $G$. The lower-number-two hardness conjecture. It is NP-hard to decide whether

$${\rm gp}_{\rightarrow}(G)=2.$$

The supplied text does not provide a proof or resolution, so the complexity of this decision problem remains open.