Why is the small white box near my fridge's compressor making an incessant clicking sound?
I have the same problem. Brand new fridge (Frigidaire). The same sound coming from a white box attached with ABS stamped on it. I unplugged the fridge and removed the box to examine the components. It appears to be a thermostat of some sort? It also has a little red adjustment screw in the center of the component. I am making my best guess and thinking that it regulates when the pump kicks on according to the ambient temperature?

Best guess 2, some sort of power regulator, maybe for different types of electricity? But the housing is cylindrical and the red dial is dead center leading me to believe that it is a coil inside. The dial is to tighten or loosen the spring to optimize efficiency for different climates or elevations? 

Either way, I left the box off and plugged the fridge back in to see if it would keep making the sound. The sound stopped. This tells me that it is a poor design, allowing vibrations to be amplified by the housing. A little cardboard between the housing and the metal cylinder and the sound is gone forever. I do not recommend doing this unless you have some basic knowledge in electricity, and insurance on your house..