First of all this "light" is an AC light (AC=Alternating current) Everything else in your computer is DC. (DC=Direct Current)
I'm assuming that the other lights you want to turn on and off with the same switch are plugged into a connector like this:
If you want to do it, you'll have to put all the lights on one power supply line. Then put the switch in that line before any thing is plugged into it.
Something like this:
power----Switch--split the wire----line 1----to inverter---to Cathode tube
-----Line 2----to 12v DC lights