I would suggest you get a tester like this.All lights work on the jeep when connected and disconnected. 4 pin Connection.
Edit to Add. Actual trailer wiring/lights are confirmed functional with another vehicle.
Not to be a NitPicker, but the harness is grounded, right ? Test with meter, fuse and ground, just to be sure, power to Logic Box ?Correct, this requires power to battery and is fused. Fuse is present and not blown.