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"Did you get my e-mail?" - "The biggest problem in communication is the illusion that it has taken place" - George Bernard Shaw, 1856
If the position of the reed switch is fixed (most likely) then there is probably a magnet that passes within close proximity each time a coil is wound - in which case it's supplying pulses to a counter. That's just the most likely - it could also be used as part of the safety system - disabling moving parts until a cover is closed or something similar. It's just a switch, maybe a normally open, maybe a normally closed, that's actuated by a magnet or magnetic field. inside are two pieces of metal, touching if a n.c. or just barely seperated if it's a n.o. - one of the two pieces is attracted to a magnetic field that pulls it away fron the other contact, or pulls up against the other contact, again, depending on whether it's a normally open or normally closed.
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Some days you're the pigeon, some days you're the statue.