Grey Wagtail Motacilla cinerea, Bergeronnette des ruisseaux
or Pied Wagtail Motacilla alba, Bergeronnette grise.
LR 2 2 64 p Spare my grey beard, you wagtail?
The name of these species derives from the way they wag their tails and stern up and down. Both of them display enough grey to enable Shakespeare to operate a pun on colours with "grey beard" repeated twice, in the same way he likes puns on words. This, in the absence of an elaborate stage setting, provides a background picture to the figurative meaning of wagtail in this context: Oswald is an obsequious fellow too scared to stand still. This image can be linked with a passage that follows:
These kind of knaves I know, which in this plainness
Harbour more craft and more corrupter ends
Than twenty silly-ducking observants,
That stretch their duties nicely.
(LR 2 2 98-101, emphasis added)