can you share a pic? The amp should have input power, ground and signal. Signal would be accessory power - like the radio. There’s a signal wire at the rear speaker harness. Even if you use speaker level inputs, sometimes the signal isn’t enough to get the amp going, so the signal connection does it.
Amp power and ground should be home runs to the battery to be “most correct”, that said, the kenwood 300w x1 is only 30a and there’s a 10 gauge multi-strand source at the inverter and you could get a good enough chassis ground in the rear of the cab. I would not advocate this on a large amp. I’m mentioning it; I have battery home runs.
Amp out should be speaker wires that connect to the sub.
Is the Amp powered on when you turn on the accessory or ignition or the radio button ? There should be an LED power indicator or ‘on’ indicator. Is that on when you turn on the radio? If it’s not, check the signal connection at the amp, see if it has +12v. If not, you can try to feed it to get the amp to turn on and see if the sub resumes working.
A point of clarification: You mentioned previously that you checked the FORSCAN values for the stereo; 7 speaker, sub, and that aftermarket sub is selected.
did you --change-- any forscan values for the sync install?
you mentioned above you have power at the amp power lug.
Do you have a ground at the amp ground lug?
The reason I ask is I had a ground cable fray on me, giving me a condition where my amp cut out and stopped. I had ‘ground’ but not enough for the amp. When I re-ran the ground it worked and when I checked the existing ground cable I found the strands had frayed and broken!
