I imagine there's a metal arm or pivot moving just inside the housing, which you could detect with a strong magnet. And the magnet may produce waveforms in a coil of wire placed next to it, or wound around it.
There's even a slight chance the motor can induce waveforms in the coil of wire (directly without need for a magnet). Amplify the signal. It's possible that the motor's current draw jumps up or down at certain positions in the cycle, which you could spot as a peak or a trough.
The above suggestion assumes the housing is plastic which allows a magnetic field to penetrate. If the housing is steel then it won't be easy unless you can find a particular spot that works for you.