The 'wad of gum' is the melted coil sleeve. You will need a new coil, and a new sleeve. That sleeve is one piece, extending throught he coil. The small flange is at the top, and the longer part is at the bottom to guide the core.

That whole assembly is (probably) mounted so that the bracket and coil core (moving metal rod) are vertical, with the rubber pad at the bottom. Courtesy of gravity, the coil core rests on the rubber pad. When the coil is energized, the core is pulled up into the coil. As the core is moving through the coil, the power to the coil is switched off and the core continues moving up via its inertia, until it hits the upper bracket and makes the 'knock'.

If that bracket is mounted horizontally in the game, then you are missing a return spring, but then the core would have a flange on it for the spring, so I thnk it mounts vertically.

The transistor that energizes the knocker coil is also no good anymore (it's shorted), that's what caused the coil to overheat and melt the sleeve), and the pre-driver transistor that goes with the driver transisitor is probably also no good.

Hope this helps.

Don C.