Okay, now I'm (almost) as confused as poor Tony.

To make it easier to poke at the problem, I dug out a spare docking sled, and just wired up the yellow+orange to +12V and the black to GND. The aim here being to reproduce the in-car behaviour exactly, without having to wire-up the serial port behind the dashboard of my car.

Well.. no problemo. Works perfectly, in/out of standby.

Ugh.