Possible Clues:

• Something curious
• Strangeness of headless corpse Inspector West finally cracks
• Eccentricity that's not easily explained
• Do tidy (anag.)
• Strange eccentricity
• What’s rum? “Alcoholic drink without head” should capture it
• Rarity in title given for Major Tom’s exploits?
• Peculiar thing -- revolutionary party with heartless song
• Peculiar trait
• Take too much vermouth during day periodically? This is rum