So, I'm wondering if I got a bum unit or if I'm completely missing something...

I recently installed a factory-new 8000NEX in my 2012 Mustang and cannot get my subwoofer to work. This is not a factory sub, so all the wiring is my own and it's not a harness problem (I.E., harness not powering the factory sub, etc.)

I have the remote wire going to the amp, and the amp is powering on (power light comes on). I also have the RCA cables plugged into the outputs on the back of the unit and going to the amp. I'm using (what I believe are) the two subwoofer RCA jacks just below the backup camera (labeled SWL and SWR).

In the 8000 settings, I've turned the sub on.  However, although the amp powers up, it does not output any sound.  I will note that this setup worked without issues on my prior stereo and that none of the wiring changed when I put the 8000 in.  Just for testing purposes, I put a new RCA cable in to see if my cable got messed up somehow, but it still doesn't work.

Is there a setting in the radio that I've missed? Or did I get a unit that's broken?

Are your HF speakers powered through line outs (rca) and separate amp?  If yes and working, a quick test method for your sub system being functional is plug your sub rca's into the HF outs and make sure the HPF is below your sub system's upper frequency threshold.

Otherwise you'll need a separate line-level source to verify which is malfunctioning.

Plug direct into rca's with a MP3 player and adaptor see if amp works. Sounds like a setting issue. 

Plug direct into rca's with a MP3 player and adaptor see if amp works. Sounds like a setting issue. 

Hmm...why it did not occur to me to do this, I don't know...

I plugged into the amp with my iPhone and an RCA adapter and get...nothing.  Apparently, this is an amp issue, not a radio one.  Which, I guess is good news.