Using your own schematic:
+5V --10K -|>|- G -|<|- 10K -- +12V
If the diodes were replaced with LEDs, then in theory when the switch is closed, one LED would be connected to 5V and GND with a 10K resistor in series, and the other with be connected to 12V and GND with a 10K resistor in series.
I suppose the first LED wouldn't light, because if the switch is closed, the regulator would shut off so there would be nothing to supply 5V. But the second should light. Even so, it now occurs to me that that would be the opposite of what one would want. :-)