As Robert said, the neon lamp within that switch requires a high voltage load (120Vac or higher) to illuminate. Therefore, it would only illuminate if connected on the AC input side of your power supply, not the 12V DC output side.
If you want a switch to light up on the 12V DC side, you will need to use a different switch.
Here is essentially the same switch with a 14V nominal (12V will suffice) incandescent lamp:
If you prefer LED indication and can tolerate a different form-factor, we have a round type rocker switch which will handle your current requirements and light up with 12V in the following part number: