Beeping light fixture
That beeping puts me in mind of the beeping you get from a smoke detector that has a low battery.

Are you absolutely certain it's the fixture?  If so, look for some kind of battery backup - maybe there's a night-light function, or a wireless remote or something?  Or a built in smoke detector I suppose is a possibility.

Anyway - find that and change the battery.  And look around the fixture for smoke detectors, maybe your ears are tricking you on where it's coming from.