Most likely the defrost timer switch. All older fridges will eventually need one. Remember what it was, and the next time you can do it yourself. The next thing to go might be the icemaker. But, they are easy and cheap as well. Other than that, there isn't much else to break on an older fridge except the compressor itself. Everything else is pretty easy to fix.
You’re quite correct. Defrost timer switch.
The fact my bar mini-fridge doesn’t have one may be why it has been running longer than most people I know have been alive.