Driving EL wire from button push on a gamepad
Depending on your EL driver box input voltage, you have a few options. All are based on usign a simple P-channel MOSFET as a switch. Note that all values and part numbers are just guidelines, any general purpose NPNs will do, similarly any general P-ch MOSFET will do (as long as it has a low enough threshold voltage, e.g. &lt; 3V or so, and can handle the maximum EL box current easily - check the rating)
Also resistor values are not set in stone, you have considerable leeway with the values here also (the 2.2k&Omega; R_PULLUP is a guess at the gamepad pullup)
For example, R1 could be anywhere between, say, 10k&Omega; and 1M&Omega; (the higher the impedance the more prone to noise, the lower, the higher power consumption and the harder for the transistor in the last circuit to pull down) 

EDIT - Okay, now we know the voltages, then we can settle on this circuit. I will leave the rest of the circuits below in case they are of any use to future readers.

This assumes that the EL wire driver supply is always a bit lower than the gamepad supply:

 

Make sure you choose a MOSFET with a low Vth (turn on threshold voltage) and use a schottky diode (make sure it is the right way round) The EL Driver supply and Gamepad supply ground wires need to be connected. The Switch represents the button, R_Pullup the assumed internal gamepad resistor, and the +3.3V represents the gamepad supply. 

Simulation:





Circuits below left for interest to future readers

If the input voltage is +3.3V, then things are very easy, this circuit will work (note - this assumes two 3.3V regulated supplies that are not going to vary by more than a couple of percent):



EL_BOX is a simple representation of the load from the EL driver box. When the button is pushed it pulls the gate of the P-ch MOSFET low and turns it on, supplying power to the EL driver.  

Simulation:



If the voltage of the EL wire box is different, let's say 5V, then if you can hack a schottky diode in between the button and it's +3.3V connection, then this circuit would be an option:



The diode prevents the 3.3V rail interfering with the 5V rail, but still allows both to be pulled to (near) ground. A schottky is used as it has a lower drop than a normal silicon diode, to make sure the game controller IC pin sees a logic low.  

Simulation:



If it's not possible to hack the diode in (i.e. all you have access to is the +3.3V line and ground line) then you will need a couple of transistors to invert the signal something like this:



You could use N-ch MOSFETs for Q1 and Q2, but bipolars are cheaper so unless you need the lowest power consumption NPNs will do fine.  

Simulation: