Product review (5 stars): So that was the problem.
Bought for a Kitchenaid KBFS25EVMS0 that was making a frequent clicking noise, and cycling off for way too long at a time - freezer was set to 0 but rising as high as 17 before the compressor would cycle back on. After realizing that I hadn't cleaned the dust out of the coils in a while, and after cleaning out the thick blanket of dust, I did enough internet research to determine that this was the part that needed replacing. It was an easy swap. Once you unscrew the back cover, you just need to remove this thick wire that acts as a sort of bracket, then unplug the stuff that is attached to the old part, unplug the old part, plug the stuff into the new part, and plug in the new part. Replace that wire bracket thingy (the most annoying part, but still not too annoying), put the back cover on again, and plug back in. I think my fridge was unplugged for 5-10 minutes while I did that. The clicking noise is gone, the temperatures in fridge and freezer are constant, and all are happy in my house until the next thing happens.