Since the only power coming out of the brick while it is on standby is whatever you can draw from the 'trigger' pin, the only power available to light up the LED is whatever you can draw from the trigger before the brick turns on. That current may be too small to provide any useful lighting.
Assuming the trigger can provide at least a few mA at whatever voltage your LED needs before the brick turns on, the way to wire it would be to put the LED with a current-limiting resistor in parallel with the switch. When the switch is open, the trigger voltage/current gets applied to the LED and when the switch is closed, the trigger is shorted to ground to turn the brick on.
If the trigger is operated with nano/micro-amps, you will not be able to produce any meaningful light with it unless you use a pulse circuit to dump charge from a capacitor into the LED but depending on how small the trigger current is, your 'standby' LED might only be able to pulse a few times per minute due to the capacitor's long charge time.