Electronic – How does this slide switch work

It is not really clear what you are trying to do. If I ignore the bit about "current flowing" then it looks as if you want a signal that indicates there is motion of the "motor." Are you actually trying to detect a motor moving, or some other object? Different methods can be applied in either cases.

Inferring that you are trying to detect that some object is moving in a repeatable fashion and you need to do so without physical contact with that object, my suggestion is attach an object that can be detected to the moving part and put a sensor on the fixed part.

If the moving part is indeed a VCR cassette, then a magnet is a bad idea as it will affect the recording on the tape. So let's use a reflector on the moving bit and a reflective optical sensor on the fixed part. The sensor looks like this

Similar sensors can be purchased here. They combine an infrared emitter and a photodiode. The light goes out the emitter, reflects off the sensor and is detected by the diode.

That sensor will produce a pulse on the output when the reflector is seen. To extend the length of the pulse so it lasts for a full rotation before being triggered again, a circuit called a one-shot multivibrator can be used

This circuit will provide a constant signal as long as the rotation continues. After one full period without the rotating sensor being detected, the signal will shut off.

Hope that helped.

Typical configuration very close to Dave Tweed answer (DPDT) except that if I understand your question properly, then your switch handle has 3 positions and not 2 (DPDT) My guess is that the two middle pins are the Common pins. Sliding the handle to the right for example, would connect each common pin to its respective end pin on the right. If I am correct then your 3 position switch should show no connections between any of the 6 pins at all when the slide is in the middle. Easily checked with a ohmmeter BTW I never saw a switch behave as per your assumption