I might be able to help - does the inside of the gum resemble these electronics?
This is from a shocking pen, but it may be the same circuit. There is a coil, a microchip, 4 watch batteries and a switch. Older shocking devices didn't have the chip, they just used a more complicated switch, generally a ratchet and pawl assembly which often broke when someone dropped the horrible thing. Newer ones just suffer from broken wires and contacts, you might be able to solder something back together.