It doesn't sound like especially smart behaviour, because  it is very common. Many birds are fascinated by their own reflections and will fight them bitterly, sometimes till the shiny surface is blood-spattered. (If that happens to a shiny surface of yours, the best way to stop it is to smear it with a bit of soap or similarly harmless material, to reduce the reflectivity.)

Your little bird seems to be a less physically pugnacious species or gender, vainly trying to elicit appropriate socialising behaviour from its own reflection.