Would you consider creating a cone light option like what you would see from a flashlight?
Viewing post in [CGMZ][Beta] Light Effects for RPG Maker MZ comments
Ah ok, I see what you mean. I thought you just wanted a different shaped light.
In that case, no it would not turn with the character. You may be able to event it by setting up 4 lights, and changing the light id assigned to the player based on the direction they are facing. But I can look into adding lights changing with direction of the character they are tracking as a feature in a future update as well.