crested flycatcher, peewee
鶲 refers to a specific type of bird: the crested flycatcher, also known as a peewee. It is a bird name with no broader abstract meaning.
鶲 combines 翁 (old man) and 鳥 (bird). The character was created to name a specific bird, likely the crested flycatcher, but the exact reason for using 翁 is uncertain.
An old man (翁) is watching a bird (鳥) with a crest on its head. That bird is the crested flycatcher, 鶲.
For ひたき, imagine the old man (翁) saying 'He took a key' (ひたき) to open a birdcage and release the flycatcher. The phrase 'He took a key' sounds like ひたき and ties the old man to the bird.
—
northern wheatear (Oenanthe oenanthe)
Asian brown flycatcher (Muscicapa dauurica)
red-flanked bluetail (species of flycatcher, Tarsiger cyanurus)
common redstart (Phoenicurus phoenicurus)
common stonechat (Saxicola torquata)
Old World flycatcher (any bird of family Muscicapinae, esp. the typical flycatchers of subfamily Muscicapinae)
narcissus flycatcher (Ficedula narcissina)