I'm guessing that I've got my wires crossed somewhere. Can anyone give me some pointers?
Yes, it sounds like you might have some wires crossed somewhere. Here is how it should be connected (assuming you have an empeg mark 2 or a Rio Car):
The yellow wire on the docking sled should be connected to a constant 12-volt source of power. This is sometimes called the "memory" wire. This should get 12 volts whether the key is on or not.
The orange wire on the docking sled should be connected to a source of 12-volt power that is only on when the key is on. This is sometimes called the "ignition" wire, and if you are using an adapter harness, it is often indicated by a red color on the adapter.
The blue wire on the docking sled should be connected only to the blue remote-turn-on wire from your amplifier, and should not be connecting to any 12 volt power sources in your car at all.
The power for the amplifier should be coming directly from the car's battery terminal (through a proper weatherproof fuse block close to the battery), and should not be connected to the adapter harness.
Your description makes it sound like your amplifier might be connected to the ignition wire, and that the wires supplying the power to the empeg are not connected right.
It could be something else, such as
this, or one of the other things listed in that section.