Possible Clues:

• Hat for country-and-western singers, Texan oil magnates, etc.
• Keeps suggesting retaining headgear
• Style of hat
• Hat, for Texan oil magnate, say
• Instruction to keep writing on relative's hat
• Topper at a dude ranch
• Not a bowler in Test troubled boy
• High, wide-brimmed hat
• Hat for Texan oil magnates etc.
• Cowboy's hat? Put it back, boy!