I don't know which club is honored by this cocktail. There's a Pegu Club Cocktail and a Clover Club Cocktail... maybe this is a generic cocktail for all clubs where gentlemen sit about smoking cigars and saying "Splendid! Splendid!" in well-aged baritone voices.
In any event, this cocktail is all about quality ingredients. It's just gin and sweet vermouth. There are so many interesting American gins that this formula fits a near infinite range of drinks.