Oh boy, the fact it spins 360 over and over point to it being a rotary encoder. The description \"transducer encoder\" also points in that direction. Still, it having only 3 terminals is a bit of a mystery.
Do you have schematics for the machine? I wonder how its depicted in the schematics?
By chance, is there a twin used for spindle override? If so, a little probing with a oscilloscope could tell the story.
Is it completely bad or just intermittent?