Fixed-point implication for the Algebraicity Conjecture

Let $G$ be an infinite simple group of finite Morley rank, and let $\alpha$ be a generic automorphism of $G$. Let the group of fixed points of $\alpha$ be $\{g\in G:\alpha(g)=g\}$.

Fixed-point implication conjecture. If the group of fixed points of $\alpha$ is pseudofinite, then $G$ is isomorphic to a Chevalley group over an algebraically closed field.

This conjecture is intended to establish the converse direction to the implication from the Algebraicity Conjecture to pseudofiniteness of generic fixed points. The source gives no resolution, so it remains open.