There are many signs of a failed refrigerator defrost timer. Some of these are an inability for the refrigerator to go into a defrost cycle and revert back to cooling, the refrigerator defrosts all of the time, or the refrigerator doesn't defrost any time.
A failed refrigerator defrost timer will usually result in a temperature change within the refrigerator. This is the first sign that the defrost timer isn't working.
The next thing to investigate is the refrigerator's cycling. Does it go into a defrost mode? Does it revert back to cooling? When a refrigerator defrosts, it goes back to its factory set temperature, usually around 55 degrees Fahrenheit, and when it resumes cooling, the refrigerator should be at around 34 degrees Fahrenheit.
Placing a thermometer within the refrigerator can clearly indicate the changes in cycling, and if a refrigerator defrost timer needs replaced.