That changes things. The reel can stop with the magnet near or away from the switch, so what you want is an AC-coupled missing-pulse detector (retriggerable monostable multivibrator), gating an oscillator, driving an LED and beeper.
A fun part for something like this is a flashing LED, an LED with a flasher circuit built in. One of these in series with a piezo beeper gets you both light and sound with very few parts. All that is needed is the monostable, which can be two small MOSFETS if you want to eschew integrated circuits.
ak