Diagnosis
That's the sound of the PTZ (Pan-Tilt-Zoom) motor trying to recenter or recalibrate. It often gets stuck in a loop if the camera's physical movement is obstructed or if there's a software glitch telling it to go to a position it can't reach.
How to Fix It
First, physically check the camera. Gently move the camera head with your hands through its full range of motion—pan left/right, tilt up/down. Feel for any snags or resistance. Once you've done that, give it a hard reset. 1) Unplug the camera from power. 2) Hold down the sync button on the back. 3) While holding the button, plug the power back in. 4) Keep holding the button for another 10 seconds until you hear the startup sound, then release. This forces a full recalibration of the motors.
If That Didn't Work
The issue might be tied to a specific Activity Zone or tracking setting. In the eufy Security app, go to the camera's settings, then to "Pan/Tilt/Zoom." Turn off "Auto-Tracking" and delete any custom Activity Zones you've created. See if the noise stops. You can try re-enabling features one by one later.
Heads Up
Avoid placing the camera where curtains, blinds, or cords can drift into its field of view and trigger constant auto-tracking attempts, which can wear the motor out faster.