Possible Clues:

• Topper made from the jipijapa palm
• Protection for head of state in Central America
• Straw topper
• *Headwear that originated in Ecuador, surprisingly
• Criticize a religious leader a degree less for informal headgear
• Father joins Hindu sage, leaving mother to carry an item of headgear
• Tile and slate are hard with a dull coating
• Summer head topper
• Plaited topper
• Unexpectedly, it's usually made in Ecuador