Its been a long time since I played around with 'ray gun' circuits but a simple one can be made from a 555 and a few other components.
This one doesn't really need an on/off switch. R1 and C1 form a simple charging circuit. Once C1 is charged (apart from a small leakage) the current taken from the battery is minimal.
The switch needs to be spring loaded (trigger switch) so it returns after 'firing'.
R2 limits the current through the LED to a maximum of about 10mA. The 555 is connected as an astable oscillator with R3 and C2 determining the frequency. (these can be changed to suit). The output of the 555 is AC coupled to a 64R speaker through C3. (If there isn't enough volume you can try taking C3 out and directly connecting the speaker.)
When the trigger switch is closed the energy stored in C1 turns on the LED and energizes the 555 oscillator. The voltage across C1 will decrease quite rapidly causing the the frequency of the 555 to fall (a sort of voltage control monostable pulse) giving a 'pew' type sound.
To reload the trigger is released, the capacitor charges and you're ready to go again after a short charging time (R1C1)
For a 'machine gun type effect' operation.
C1 can be charged by a low frequency 555 astable (around a few hertz with say 80/20 space mark ratio). This 555 would be operated by a push to make switch connected between the 9V supply and pins 4 + 8 of the IC.
As is true for a lot of projects on this site that use discrete logic, this could be done with a microcontroller instead with fewer parts, but that would also require the person building it to know how to program (which they may not), and to have the necessary development environment set up, including the hardware to program the microcontroller.
Looking at the table that was added to the OP, one can see that there are times when the system is either activated or not activated and both Wire 1 (GREEN_LED) and Wire 2 (RED_LED) have no voltage on them because they are flashing due to an open zone. So if we want to run the circuit off of just these two leads, this has to be accounted for.
Looking at the circuit below, I am ORing the two input leads using a pair of Schottky diodes, and feeding them into a Supercap to hold the voltage across the gap when no voltage is present. I chose a 0.4 F (Farad) capacitor, after using this Supercap calculator. The voltage following the diodes (Vcc) will be around 2.75v,. which is compatible with the HC (but not HCT) logic family. With no input on either Wire 1 or 2, and with the buzzer on consuming 30 mA, a 0.4F SuperCap will keep Vcc from dropping below 2.5v for 0.73 seconds (which provides a safety margin over the minimum 0.5 seconds needed).
(Right click and select View Image to see a larger version of this schematic.)
Here's how it works. There are four 74HC123 one-shot monostable multivibrators (IC1 & IC3) used for timing. All are set for 1/2 second delay using a 75K resistor and 10 µF cap. Typically one would trigger timer IC3A on just Wire 1 (GREEN_LED) going high, but since the lead may be flashing, this would cause it to trigger multiple times. So I am using a 74HC74 D-type flip-flop (IC6/1) to remember the state. When the flip-flop is set, the output is fed into the B input of the 74HC123. timer. When the B input goes high, it starts the timer. The output of the timer high feeds into one of the inputs of the 3-input NOR gate (IC5), making the output low, turning on the P-channel FET and sounding the buzzer.
After half a second, the timer expires and the buzzer turns off. Even if the Wire 1 (GREEN LED) goes to 0 and back again because it is flashing, the flip-flop won't change state and the timer will not trigger again.
Similar logic occurs when the state goes from activated to deactivated (Wire 2, RED LED goes high). Again a flip-flip is used to keep state. The difference is when the top right timer IC1A expires, the middle timer (IC1B) is triggered. It simply waits a half second with the buzzer off, and then the bottom timer (IC3B) is triggered, sounding the buzzer another half a second, altogether twice per the spec.
The logic could be simplified a little, but I presented it this way so it would be easier to understand. Instead of using the two inverters IC2A/IC2B, the two unused 3-input NOR's could have all three inputs tied together and function as an inverter. In that case the circuit could be realized using just four IC's.
Best Answer
Is the duty cycle supposed to switch from 50% to 0%, or decay from 50% to 0%? Is there any particular precision required on the 50%? Is there any requirement regarding quiescent current?
I would suggest that you start by using a 555 or similar chip to generate a symmetrical sawtooth-ish (doesn't have to have straight sides) wave, and then feed that into one side of a comparator. The other side of the comparator should be connected to a circuit which will generate a voltage that will start at half-rail when the button is first pushed, but will either rise toward VDD or fall toward ground after that. If you can use a SPDT pushbutton, a simple realization of such a circuit would be to connect the center pole of the button to a cap whose other leg is ground. Connect the normally-closed contact to VDD, and the normally-open contact to the comparator input. Connect a resistor from that comparator input to ground.
Conceptually, it would be nice if a single active device could be used to provide the output, without needing the separate comparator. It's possible for the 555 to provide an output whose duty cycle will be affected by an input voltage. Unfortunately, the frequency will also be affected by the input voltage; I'm not sure of any easy way to make a compensated circuit such that the decrease in high time will be balanced by an increase in the low time so as to yield a reasonably-constant frequency (as opposed to having a device generate a 1Khz reference signal which is then shaped by a second active device). A two-chip circuit doesn't seem unreasonable, though.
Here's a simple circuit which will illustrate the concept. For simulation purposes, it uses an op amp, but a comparator would work just as well. One slight note: many comparators ground the output when the + input is higher than the - input, so the polarity would be opposite that of an op amp.