Possible Clues:

• Chihuahuan hat
• Wide-brimmed Mexican hat
• Mariachi topper
• Grave exchange of words dismisses women employed by one hiding from The Sun
• Rob Morse of his hat
• Grave or reactionary - it protects one of those at top from The Sun
• It may be felt to be over a Mexican's head
• Tampico topper
• Chihuahua chapeau
• One sported in sun, getting dark red — ominous, at first