I tried holding the power button in. After 5 or 10 seconds the radio beep beeps - but it keeps on talking. Shorter hold downs have no effect whatsoever. The manual makes no mention of a second function of the power button.
I'm pretty sure the clock display stays lit up forever with power applied to both wires. This is a 2004 vehicle, likely not using LED lights, so I figure the display is drawing the 300 mA. This is perfectly acceptable when the engine is running and nice to have. But I don't want it drawing 300 mA 24/7 when parked.
I like my new switch very much.