Works great! Trying to get the theory down so I can explain it to my advanced electronics class. If I understand this correctly, we need to look at two time frames: when the 555 outputs a high voltage, and when the 555 outputs a low voltage.
To better understand this circuit, I am going to treat the timer circuitry as two different circuits, based on the output of pin 3 of the LM555. I will also remove the components that do not affect the circuit in that time frame.
Pin 3 Low:
When pin 3 is low, the circuit would look like this the circuit looks like this:
Connecting a good transistor in this circuit will be like closing S1. Which would short out the entire parallel circuit.
Pin 3 High:
When pin 3 is high, the circuit will look like this:
Connect a bad transistor would be like closing S1. This would short out the series resistors R2 and R3, as well as the Green LED.
The diodes are in place to prevent current from flowing back int the green or red LEDs when it is not their "turn" to light.