Hey, I have this exact problem too, and it only happens when using Jago.
The squeak/beep/chirp seems to happen during the intro cutscene, when using shadow moves (aside from shadow laser sword), twice during a taunt, while activating instinct, and during instinct, it happens when using any special moves. I think it might also happen at the end of match.
Reinstalling didn’t change anything. Anyone know what could be causing this?