"Dave Plowman (News)" gurgled happily, sounding
much like they were saying:

Joined isn't a problem - you'll just have a head unit that can be used
with the ignition off. Shorting together'd just get you a head unit
that might sometimes stay on or come on when the ignition's off.
Transposed will just give you a head unit that can be switched on when
the ignition's off, but only keeps the memory when the ignition's on...

(Assuming, of course, there's no way for the ignition live to feed back
into the rest of the car's electrics.)

It's not quite that simple. Many these days will work for a timed period
with the ignition off - for when you leave a passenger in the car, etc.
Mine does.

Still that simple - a permanent live, and an ignition switched live.