On the Q 'why won't the bulb go out?', it's because of the way the mag is built. The fixed contact point (insulated from the backplate by a mica washer) attaches to the low tension coil one end via the centre screw; the other end of the low tension coil goes (via the condenser) to the mag body. The moving contact is connected directly to the backplate by the little screw on the spring. The backplate is connected to the armature spindle at the brass taper, and thence to the mag body. So both contact points are effectively connected to the body of the mag. Don't know what the resistance in a low tension winding is meant to be - an ohm or two maybe? Not much anyway.
So a bulb with an external power source put across the points will light up and stay lit, and the difference in resistance won't make that much odds to how brightly it shines. Hence something else is needed. Like a Rizla, a 1.5 thou feeler gauge, a sensitive analog meter like an AVO, hawk-like eyesight to see when the cam ramp starts to open the points . . . or a proper buzzer. But as to why your buzzer's buzz has buzzed off, I'm afraid I've no idea!