Hugo, that last comment of yours seemed to have tipped the scales in my favor.
I pulled off the bogus adapter they put on there and plugged the one supplied with the Rio and connected up the appropriate wires (ground, ignition, battery and amp-remote) and now both the Empeg and Rio Car are working as intended.
I'm really kind of shocked now because my Empeg has apparently NEVER worked properly, as far as power goes, so it's nice to see it power on when its supposed to and go off when its supposed to and more than anything else, with the amp plugged in as its supposed to, I no longer get that annoying "POP" when I plug the empeg in with the car running, or when the Empeg boots up if its plugged in when the car is turned on!
So you can't see me, but right now I'm doing the Happy Dance that it's all working correctly finally!