Looks almost good with the exception of 3 being battery. 3 should be taillights. Were possibly the lights or daytime running lights on when you took the readings?
Although even if you do have battery on both 3 and 4 it's not the end of the world. Basically you're trailer running lights will be on any time the umbilical is plugged in which is not necessarily a bad thing.
Take a picture of the battery wiring and disconnect the trailer battery. Only disconnect one side of the battery. It's not necessary to disconnect both sides.
Pull all the wire nuts and separate the wires except the large nut for the white wires and the two large red wires. You now have two bunches of wires. One bunch is the trailer lights. The other bunch is the end of the trailer umbilical.
Test to find the bundle of umbilical wires.
Slide the black probe up into the large wire nut for the white wires, this is your ground. Write down what each wire does based on what the helper is doing in the truck. If you get no readings hitch up the trailer and try again. If you now get readings you have a ground problem. Just leave it hitched for now if that's the case and continue testing.
Check the voltage on all the single wires (green, white and yellow) I'm betting they all read 0 because they (or at least the green) was fed by the trailer battery.
(color) Right turn or brake
(Color) Left turn or brake
(Color) Tail
(Color) Battery charge
(Color) Brakes
Single green
Single white
Single yellow.
Troubleshooting or additional testing:
If you're unsure of your trucks wiring or the umbilical wiring do the following.
Unplug the umbilical and unhitch the trailer.
Reconnect the trailer battery.
Take a voltage reading from single green to single white (red probe on green wire and black probe on white wire).
If you get 12v positive you know green is trailer battery power. If no power try measuring from single green to bundle of whites.
If the green wire is 12v + you can use it to connect to the different colored wires and identify what each color wire does. On the trailer side of the bundle hook the single green to a wire and go see what lights are on. Make sure to write it down.
Remember a taillight will always have the side markers on at the same time.
If the lights all work you probably have a problem with the umbilical or the ground to the truck.