[ErroneousBosh]

This is a bit off-the-wall but maybe you could use a variant of the approach used to see tiny movements in video? There you offset two clips by a frame and "subtract" them so that anything not moving just kind of vanishes, and purposeful movement shows up as a bright line.

Maybe doing something similar with a spectrogram would work? Two spectrograms, one delayed slightly with respect to the other, and subtract one from the other, and you might see bright spots that appear where the sound changes.

[OkayPhysicist]

Building off that idea, if the offset between the two spectrograms was based on the relative distance between the two mics (ideally 3), you could eliminate noises not coming from a certain point in space, e.g., the birdcage.

[ErroneousBosh]

Oh well now I'm just going to have to build something.