Not trying to steal your show JW, but:
On most single-phase compressors with a single-pole contactor, there is a solid bar on one side of the contactor instead of having two contacts. One leg of power passes down the bar to the capacitor and to the run winding. It passes through the run winding of the compressor and from common back to the contactor. It lands on the load side of the normally open contact of the contactor. At off cycle, line voltage will be read from one side of the normally open contact to the other: Line 1 on the line side and Line 2 on the load side via the windings.
The crankcase heater will be attached to the contactor with one leg on the load side and one on the line side of the normally open contacts. At off cycle it will have line voltage applied to it and will heat the crankcase. Once the contactor is energized, both the line and load side of the normally open contacts become one. Since you cannot feed a load with one line of power, the crankcase heater will not work again until the contactor opens. This is a simple way to turn the crankcase heater off during the on cycle and to turn it on at the off cycle. Exercise caution when checking this type of setup because power is always present on the load side of the contactor.