Why isn't this Elenco circuit working in Falstad's simulator?
You've got a broken connection between the transistor and the transformer where there is a red dot at the transistor collector.  Fixing this connection and then the circuit basically works; however, the timing is a bit off.  The 100uF and 100k resistors will set the time between the "clicks".   When I ran the simulation, the timing was off.  If you've entered the values and rest of the circuit correctly, then perhaps the speaker load is needed to get the timing right.  Try putting an 8 or 4 ohm resistor in to model the speaker.  Since the simulator shows the current flowing, you can tell when there would be a sound by the current flowing through the resistor.

Good luck!