Let's start with reviewing the two reference illustrations, the first showing the standard connectors as viewed from their face (mating end) and the wire color typically used for each function.
Disconnect the AC connection from the trailer (commonly called shore power even though we don't have boats)
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If you are not plugged into a TV then I would start by measuring the resistance in Ohms from each contact on the trailer connector to the frame of the trailer. If one contact appears to peg the meter upscale or downscale it is likely the Black wire contact connected to the positive battery (+) terminal. For the frame connection find an unpainted surface, bolt or perhaps use the negative terminal (-) on one of your batteries. Normally you will be able to fairly easily follow this wire to where it connects to the frame. On my FF you can open a weatherproof junction box attached to the frame and see all of the wires coming from the trailer connector and the connections to each wire.
The contact corresponding to Ground (typically White) should be the lowest resistance in Ohms and will be one of the two larger wires. It should be in the position shown on the connector diagram. Keep in mind that 10 gauge wires are larger in copper diameter, can carry more current and have lower resistance than 14 gauge wires. Wires that are 16 or 18 gauge are even smaller.
Going clockwise the next contact is Blue. The resistance on this contact will be dependent upon the number and size of magnetic brakes on your trailer. I found the following specification for each brake magnet: 7 inch brake magnet resistance should be 3.8-4.0 Ohms; 10 and 12 inch brake magnets resistance should be 3.2-3.5 Ohms. These are very low in resistance and your reading should be even lower as the left and right magnets are wired in parallel which causes less resistance. It is generally easier to test that the brakes are wired correctly by using the Amp rating of your multimeter with the red lead of the meter connected to your 12V battery and the black lead connected to the trailer contact of the brake. Here is a chart of the Amp readings you should expect to measure:
7 inch Diameter Brake Drums
Max Amps at 9-10.5 Volts Max Amps at 12-13 Volts
2 Brakes 4.7-5.6 6.3-6.8
4 Brakes 9.5-11 12.6-13.7
6 Brakes 14.3-16 19.0-20.6
10 and 12 Inch Brake Drums
Max Amps at 9-10.5 Volts Max Amps at 12-13 Volts
2 Brakes 5.6-6.6 7.5-8.2
4 Brakes 11.3-13.3 15.0-16.3
6 Brakes 17.0-20.0 22.6-24.5
The contact for the Brown wire is next and connects to the Right Stop and Turn lights. As above it will be easiest to confirm that the Right light is connected correctly and working if you use the Amp connection of your meter. Red meter lead to battery + and Black lead of the meter to this contact. Have someone check that the Right light illuminates. In the old days you could use the Ohm function but with LEDs and the small current they draw it is best to check the current flow (which can be a few Amperes or less).
The contact for the Black wire is next. Changing your meter to Volts, measure the voltage on this contact with respect to the frame. You should measure the battery voltage. If you read zero then perhaps the fuse which is normally in line with this trailer lead has failed (open circuit).
The contact for the tail lights and license is the Green wire. You can test this with the Amp function of your meter as you did with the Right Turn light above.
The contact for the Red wire is for the Left Stop and Turn light. Test this as you did for the Left.
The only remaining contact is the center, which is the Yellow wire if used. I have only seen it occasionally used for backup lights on the trailer.
Hopefully I have not made any mistakes and I rely on my comrades here on the forum to confirm or make any additional comments and corrections.
Good luck!