First we should sort out what you tested. If the only thing that came on was the 12V power then that is normal. Make sure you actually turned on your turn signals, brake lights, etc. or the test lights won't receiver power to light up. This can be seen in the video below for the # C66NR. Assuming that is what you did then yes, I would say the issue is on the vehicle side.
Since it is a factory connector it can be replaced with the # HM40975. However, before replacing it I would test... view full answer...
It may not be your 2012 Nissan Armada that is the problem. Since you already checked relays and fuses go ahead and check the connector on both the vehicle and the trailer. Make sure there is no damage or corrosion, clean as necessary. Once this is done, go ahead and test for power on the vehicle side connector with a circuit tester like # PTW2993. If you don't have power here test behind the connector and then work your way back to identify the problem. It could be the connector which could... view full answer...