A very similar badge, but depicting a silver pheasant, was sold at Christie's New York, The Imperial Wardrobe, Fine Chinese Costume and Textiles from the Linda Wrigglesworth Collection, 19 March 2008, lot 28.
The crane was thought to live for over 200 years and stored its accumulated wisdom in its red 'cap'. This is probably why the emblem of this bird was used for the emperor's closest advisors.