Initially I noticed that the freezer and refrigerator were not cooling well, not staying consistently at their temperatures. It took a few days for it to completely stop cooling.
However, the fan was still blowing out the back of the unit. The air was still blowing inside and the coils were not frosted over.
In addition, I could hear the compressor "trying" to turn on. I could hear a click, then the compressor would start humming, but very "slowly" like a car trying to turn on but failing. Then it would kick back off after a few seconds of trying and failing to kick on.
This relay and capacitor solved the problem. However: they did not visually look like the same relay and capacitor. They are different than the original ones on my Amana unit from around 2011. The clip that held the old relay and capacitor on did not fit on these new ones, so they are just held on by friction on the pins.
This was an easy repair, once I confirmed that this relay and capacitor really were the correct replacement pieces despite the different shape and color.