Humming noise from under hood

It sounds like air in the inverter cooling system that has a bleeder valve to clear it. But the part that you're shaking is the throttle position motor, which I've never heard making that noise and is not related to inverter cooling.

 

That link only shows as a still thumbnail image for me, but would you by any chance describe the "humming" as maybe a whine, kind of buzzy?

The throttle motor does indeed make a whiny sound when the car's in READY mode. It is positioned by the ECM sending a square-edged train of electrical pulses to it. The pulses are sent at a frequency humans can hear, and square waves have a whiny, buzzy sound to them. And the throttle actuator is, of course, a motor, just the thing for converting incoming electrical currents into slight motion, in this case a whine.

If that's not the sound you're describing, then we might be thinking of different things.

 

In the video when they wiggle that motor the sound goes away... On the push, but not on the pull... But the sound doesn't sound like that motor in the video. It sounds like air in the inverter cooling system sound, which of course likely would not go away by pushing on that motor.