I had to think more, sorry for the quick note earlier.
Well, here is where you may run into a problem with those switches. I would not be surprised that they switch to Positive, 12 VDC. Thinking Black is ground, Red is input power, White is output power. Easy enough to verify that with a battery and LED.
If you are trying to turn on the stock lockers, they want a Ground input to turn on the locker. All you really need for that is a two wire switch with ground on one side then closed sending ground to the locker wiring on the other. To have that light up becomes the problem. You either need a DPDT switch with a light where you can do the ground switching irrelevant to the switch having a light on it. Something to that effect. So that is not the switch you got... Your switch would turn on a solenoid for a ARB locker or similar 12VDC triggered item.
You can take the switch you got, run it to a relay that is positive switched. Then have the relay contacts close the ground loop to activate the locker. That while another thing to install, will help keep those switches.
Orrrrrr, forgo the lighted aspect of the switch and just run a ground through it. Again, thinking that will close via the Red and White wire. Again, easy to check with a LED and battery, an of course with a meter. You just would not have lights on the actual switch at all, hence no power.
They didn't make the stock locker simple with aftermarket switches.