Putting the above suggestions in order might make your search easier. First buy a simple "trailer light tester" and a 12/6volt test light. They typically cost about $5 to $10 dollars apiece in almost any parts store. NAPA is nationwide and carries them. Most typically MoHos have one of three outlets prewired, a four, six or seven conductor outlet. Buy the trailer light test that fits your rig.
Plug the tester in and have someone operate the lights, have them turn on the parking lights, the appropriate light should illuminate on the test plug. Have the headlights turned on, the test plug light should remain on. If the light comes on, have your helper turn the headlights completely off.
Now have your helper apply the brakes, "Two" lights should light up. If they do, have your helper turn on first one directional flasher and then the other.
If all works, you now know the wiring in your rig is working correctly and now you can connect the umbilical cord and retest.
If all works, you now know the problem is in the towed vehicle's wiring. If the test plug lights fail to come on when the test plug is connected directly to the RV's outlet, check fuses first. The chassis manufacturer should tell you where the correct fuses are and using a 12 volt test light check the fuses.
If no blown fuses are found, carefully disassemble the outlet, being careful not to drop any of the set screws, they don't sell spares.
If any of this confuses you, find an auto electrician to check out your rig.
The correct color code for wiring tail and brake lights is, White = ground, Brown = taillights, Yellow = left turn signal and Green = right turn signal. This is the STANDARD color code, any mods should be corrected to make maintenance and repair easier.
Black is not chassis ground in trailer light cables or connectors.
The other wires are used for other functions not mentioned in your post.
For the layout and colors code for all typical connectors go to the following link;
LINKOn edit I found that I forgot what to do if the umbilical cable fails, if it has removable connectors disassemble the connector and check continuity, Oh Oh, now you need either some long test leads to connect to the battery(or any 12 vdc point or a VOM or DMM with a continuity or resistance scale.