I figured it out! Or I figured out a workaround at least.
I subtracted the head’s rotation from the eyeball’s rotation and got the eyes to look where I wanted them to look.
I put a socket on the nose bone between the eyes then used the “Get Socket Rotation” node in the “Character Blueprint” on that socket.
(See picture below)
I did the math using blueprint nodes to get the difference between the initial socket rotation and the rotation after the head turns.
(See picture below)
Then I plugged the resulting rotation into the “Transform (Modify) Bone” node in the “Anim Graph” of the “Animation Blueprint”. This basically neutralizes the eye’s rotation so no matter how the head is rotated, the eyes will look straight ahead. Then I plugged the "Look At node into the back of the “Transform (Modify) Bone” node and it worked.
(See picture below)
