Remote Wire Hookup for Sub / Amp

For my Gen 2 2005 Prius;

I have tried to tap into the grey wire in the stock amp under the passenger seat but am not certain this is correct. Can someone confirm the best way to wire the remote wire for an amp and sub? I have not replaced the stock stereo system and would entertain tapping into a place in the back of that, if that would work. The end result of leaving the system set up, working as is, is that I have to turn the car on, then off, then on again for the amp to turn on. It works at that point, but I suspect this is not all so good as far as a healthy set up is concerned. The red amp light remains off once the car is off, but sometimes when I open the door, or roll the window down the amp kicks on, if it is not already on. Seems like some wiring problem, and I'm guessing the remote turn on wire is the culprit, as I know I have not set it up correctly. Thank you!

 

That elusive remote wire! I found a couple of threads where it's described that often the center console power outlet is tapped for amp signal. I attached the sections of the threads;