Is there any reason not to hook up another 12volt device (e.g. a 12v refrigerator compressor) to one of the pump monitor inputs? That would let me see how often the Refrigerator cycles on/off.
Absolutely. A fair number of installs have done this to monitor cycle times. The only thing to be careful of is that fridge compressors can sometimes generate voltage spikes, so you’d definitely want a quick blow inline fuse rated at less than 1 amp (or other over-voltage protection).
This issue tends to be worse on older equipment, as more recent 12 volt units often have quite good built-in transient voltage suppression.
It can sometimes be a little tricky to know exactly what contact point to monitor, as some fridges will always draw 12 volts, just at low amperage when not actively cooling. You want to use a multimeter to find a connection point that shows 0 volts when compressor is off and positive (generally 12 volts) when compressor is running.