Why does my Kenmore refrigerator run continuously?

My Sears Kenmore Coldspot refrigerator (Model 106 7647264) runs almost continuously. Ice is building up in the rear lower panel of top freezer.

It is over 30 years old and housed in our cabin. It is turned off each time we leave the cabin and stays on about 2-3 days when we are at cabin. This time it has been on for over 2 weeks. When we first got to the cabin 2 weeks ago, it cycle on for 20 minutes and goes off for 5 minutes--normal stuff. I keep turning the temperature setting (scale of 1-5) lower and it still runs continuously with stopping)

The coils, etc are cleaned--no dust, etc.

I will next disconnect and defrost the ice from freezer. I do not know how to tell if the timer or thermostat is defective. I think I read that I can advance the timer clock wise until it clicks? (I assume this turns on the heater in the freezer?)

Is there a safety factor (like starting a fire) if unit keeps on running without stopping?

Thanks