Yes Basil will sometimes do this if he is on his high perch and the light throws a shadow, he will dance with it..extend his foot to the shadow and
offer his head to it while making soft whistles..
He normally only does it for a few minutes though.
One of my budgies loves to talk, and play with her reflection in a mirror. It's a full length mirror mounted on a door, and she goes over there whenever she's on the floor in that room. I am a believer in no mirrors in cages. So, that's the only one she can get to.