So does the UHaul plug have green? I would assume UHaul only has something like this with green, yellow, brown, and white:
So the black wire that is left is coming off the car somewhere?
Anyway, the test lights should come on for turn signals and running/stop lights. Doesn't have to be hooked up to anything else. If you've got no lights on the tester, then the ground is likely bad. If you got all lights but the RTS, then something is foul with that black wire.
You could get a couple dollar test light at the auto store to do more testing. You can ground the tester, then insert the pointy end into the trailer connector and check for 12V. If you check the green, yellow, and brown and the light comes on, then put the ground of the test light in the white hole and check again. If you see nothing, then the ground is bad.