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With that said, your cut and paste of the URL failed. So, I have to kind of guess at some things. You said PDP stick for PS3; I’m assuming you mean the Mortal Kombat stick.
If you’re starting with that and want them lit, the buttons from paradise you would want are these:
And you’d need to get one of these for each one you want lit.
There are other lamp lit pushbuttons, where you likely saw the 12v. You do NOT want these for an arcade stick. The PS3 only provides +5v of power, and converting it up to 12 to power lamps is a very bad idea. Those 12v lamps are for arcade cabinets with the serious power supplies, NOT for arcade sticks.
Now, wiring it up, whole 'nother ball of wax. I can’t help there because I have no information on the electronics inside the PS3 MK stick. Find me information on it, such as whether its common ground, and I can tell you more from there.