What's causing occasional loud clicks, but fridge is still working?

My Kenmore Coldspot (mdl#: 106.78222801) has started occasionally making a loud click when the compressor starts (a few times a day). I've cleaned the coils underneath as best as I can (I've cleaned them before as well). I've also checked the fan, and it's clean and spinning freely. The fridge and freezer are both still cold, so I know it's working most of the time. I've also tried turning the temperature setting down to make the compressor come on, and when I do there is no click. So it's not consistently happening.

I'm assuming it's the start relay or the capacitor starting to go out? But how can I tell which it is? Or am I looking at the wrong thing?