That's not the mouse, but the CPU causing coil whine when the mouses causes the kernel to up it's CPU usage as you fly across various GUI elements.
I had a Logitech G500 with awful coil whine and the opposite problem: it would stop whining when moving and start when idle. I suspect it had to do with the power saving mode that lots of mice have, where the laser power supply ramps down to dim the laser illumination after a period of no detected motion.