I think you can replicate the Kepler Light Curve of KIC 8462852 AKA Tabby’s Star using the Gyroscope below.
But the real reason this won’t work? The Rotor and Center Axis have to be INSIDE the star. This is more comical than anything else.
The Gyroscope above appears to be able to replicate the light curve.
Spinning a Gyroscope unbalanced would be a catastrophe. The object would HAVE to be balanced and complete. Not under construction. Don’t worry about building rotors inside a star. ha!