Your mention of the blue wire from the empeg set off bells since I didn't see a blue wire back there.
It looks like the jerks who did the install didn't use the supplied adapter, and used their own, which doesn't *have* a blue wire. In fact, the red and yellow wires are also swapped around when compared to the docking connector. So I need to pull that funky connector off and use the one that came with my new Rio Car and re-wire it, this time with the yellow and red wires being actually the yellow and red wires, and then also connect up the blue "amp remote" wire.
But that still doesn't affect that the Rio Car comes on and then turns itself off when I have the battery/ignition wires in the appropriate places, even if they're backwards on the connector that's in there now.
These guys really f**ked up my car...