I would suspect the feedback eliminator. It digitally records the page then plays it back. The unusual sounds you describe would be the kind of thing a digital record/playback system could create if it was on it's way out. Other than that, the only thing I could think of is that the sounds originate at one or more paging locations and are being picked up by the handset when the page is made. It's also possible (but not likely because the amps are always on) that the caps (particularly in the power supply filtering) in an amp are crapping out leading to motorboating or other instability that could sound like a bird chirping. But I think it would always be there, not just after a page.

-Hal

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