Whether they have any extant function or not, they have lost their former function and in that sense they do fit the definition of vestigiality. Vestigial structures are often called vestigial organs, although many of them are not actually organs.
There are quite a few birds famous for doing ritualized mating dances, so I would only list 5: The Red Capped Manakin, The Black-footed albatross, The Western and Clark's grebe, The Superb bird of Paradise, & The Victoria's riflebird.
In the Hindu religion, the peafowl is a sacred bird An animal that has wings and is covered with feathers. Birds have a backbone, are warm-blooded, produce young from eggs, and walk on their two legs. Most can fly. , because the spots on the peacockâs tail symbolize the eyes of the gods.