You can use the strobe light curve in the express to program the channel so that it is either full on or off, but the power is still going to be noisy because of the way the dimming works and there will be 15 other channels that are being dimmed... Also, it's never a good thing to run a wall wart off of a dimmer channel... It's also not good to run a relay or any other inductive device (like a motor) off of a AC light dimmer channel.
Do you cycle the power on the beta bright or are you looking to turn it on when the show starts and off when the show ends?
The best solution in my mind is to use a 12v relay off of a DC controller. In lynx flavor, there is the mr16 (DMX) and the DSC (pixelnet). Holiday coro has some 3 channel DMX controllers and Ali express has some 27 channel DMX controllers. All of these will do ok with a relay as long as you have a diode hooked across the relay to absorb the reverse energy spike that the coil creates when you turn the relay off...
