Floating ground adapter not working in combination with KTP-445A mini amp

I heard the exact same static/noise/hiss before I introduced the amp. My old setup was the same headunit, a different FGA, and same speakers. So it's not the amp, at least not for me. I just checked and the noise is still there with the engine running but alternator charging of the house batteries is turned off. The noise does not increase or decrease with volume changes on the headunit. Volume could be 0 and you can still hear it.
 
I couldn't help myself and I wired the FGA back in to see if it has an effect on the engine related noise. I of course wired it in with the +/- inputs swapped for the RF and LR channels that have signal out on the negatives from the amp. Balance / fade still works. The engine related noise is still there BUT only if the FGA's input ground is connected! Connecting / disconnecting the FGA's input ground doesn't seem to have any effect on the music (like it did before with the mixup in +/-). So what's going on? How is it working without an input ground and why is it there if it doesn't need it? Is it because it's not actually doing it's job as an FGA since one isn't actually required with this amp as we discovered yesterday?

I have a feeling the FGA is deteriorating the signal though. I don't think it's getting as loud or sounding as "clear". It might just be a feeling since I can't swap back and forth really quickly. Is there any way to test this? Test the AC voltage in/out of the FGA? What's your opinion? Here's some closer up shots of the FGA internals.
 

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Damn, I can't remember if I checked the fade / balance with the input ground disconnected. I checked the AC voltage pre and post FGA on one of the signal wires and it went from 2.4V in to 1.5V out, so I'm pretty sure it's reducing output volume as well. That was enough to convince me to scrap the FGA!