Good idea - I took the battery on the trailer and only hooked up the ground wire for it so the trailer chassis was grounded. Then ran a temporary wire from the possitive terminal on the battery and stuck the other end of that wire in to each of the "Left brake/blinker", "Right brake/blinker", and "Tail lights" on the trailers 7 way plug and they each worked perfectly and were bright.
So I think that 100% clears the trailer as OK, and shows the the trailer grounding to the lights is good as well. I also used the ohm meter to test all 7 wires through the Reese 4 flat to 7 round adapter and they all mapped through as they should, so I think the adapter is OK.
Is there anything else on the vehicle side I should try or check before replacing the CURT wiring harness?