Is that a tan line from his hat across the top of his forehead?
Looks like face wasn’t cleaned: I’m pretty sure his hat would have covered more than that from the sun. (Though why wouldn’t he have cleaned his face?)
You’re right, a brimmed hat would have shaded more of his face. Trick of the lighting, perhaps? Or unevenly applied makeup? I’ve always wondered if his tan in the movie was enhanced by makeup.