With EMPTY refrigerator:
We found placing a HOBO XT thermistor directly on the compressor coils was the best method for determining when the compressor was active. The coils act to bleed heat rapidly from the refrigeration loop. When the compressor turns on, the heat in the coils rises suddenly and rapidly from room temperature (70º F) to approximately 100º F and is equally fast in dropping when the compressor turns off.
We tried other less successful methods before developing our latest methodology, namely using HOBO vibration sensors, AC field sensors, and temperature sensors on the compressor itself.
Our use of water in the refrigerator presupposes thermal mass as one of the leading contributors to improved efficiency. Water has a markedly higher thermal capacity than air. The use of water in the experiment also approximates what the true contents of a refrigerator might be since the nature of "perishability" is tied to the water content of food.