How would an alarm button work in a bathroom scale?
The metal cylindrical component is the lower left is a crystal. The crystal oscillations are used to create an accurate timebase.

The black epoxy blob in the center covers the fragile bond wires of an integrated circuit (IC). The IC is probably a microcontroller. Most microcontrollers have internal timers to create delays, but the delays are relatively short. To get long delays, software takes over. 

Reverse engineering an IC is extraordinarily difficult. With a lot of money and motivation it can be done, but you need specialized equipment and very experienced people.