I'm probably showing my ignorance here, but I believe you still have full voltage going through the switch, it is just a less draw (amperage?).
The 12V (well, maybe as much as 14v+) through the switch is used to trigger the relay, which in turn energizes the lights with a bigger guage wire that comes more from the battery through the relay (the relay is essentially treated as a remote switch activated by the stock switch). The power to the lights doesn't have to make the long trip to the dash switch through that small wire.
This eliminates some voltage drop to the lights, but also prevents the major juice from going through the switch. Reduces it to something like .10 amps vs 12-14 amps.
At least that is how I understand it. But I am a shadetree mechanic not a real one.
Looking forward to being educated...
Charlie