I would think the easiest way for the OP to check the plug would be to pin out the plug on the truck he tows the trailer with. He could draw a simple diagram of what pin does what then go to his MH and do a comparison of the functions.
We are all probably assuming the truck and the trailer are wired in the standard configuration. Over the years I have been in the Auto repair business I have wired hundreds of vehicles and trailers. I have run into some situations where someone really messed the wiring up. In those cases I strip everything and start completely over.
Before proceeding with the following tests the 12V. test lamp must be connected to a known good ground on the tow vehicle.
IF, note I said IF, the wiring is standard the OP should see the pin at 1 O'clock light a test lamp IF the plug is wired for a 12 V. feed to power lights, or recharge a battery in the trailer or towed vehicle.
The pin at 3 O'clock will be the feed for the right turn signal. The test light will flash when the turn signal on the tow vehicle is activated with the ignition on. The test lamp should light steadily when the vehicle brake pedal is depressed. The light will be bright.
The pin at 5 O'clock is the electric brake feed. When the brake pedal is depressed the test lamp should light. It may be a faint light or a bright light depending on the gain adjustment on the brake controller inside the tow vehicle. If the tow vehicle has a brake controller. No controller then no light.
The pin at 7 O'clock is a ground. The test lamp should be connected between a 12V. source on the tow vehicle and this pin. The test lamp should light. Note: If the test lamp lit when the pin at 1 O'clock was touched this pin can be used as the 12V. source for checking the ground pin at 7 O'clock. Simply connect the test lamp between the two pins.
The pin at 9 O'clock is the left turn signal feed. With the ignition on and the left turn signal activated the test lamp should flash. When the tow vehicle brake pedal is depressed the lamp should light and it will be bright.
The pin at 11 O'clock is the running lamps. With the running lights turned on the test light should light brightly.
The center pin is quite often wired for back up lights. If the trailer has back up lights this pin has to light a test lamp when the gear selector in the tow vehicle is placed in reverse. The ignition must be on. ( on some newer vehicles the engine must be running for the back up lamps to work). When checking the back up light circuit all precautions must be taken to prevent the vehicle from rolling. The aid of a helper would be advised.
I agree with those who have said there MUST be a converter either built into or added to the tow vehicle in order to make the brake lights function properly on the trailer if the tow vehicle has turn signal lamps independent of the brake lights.
In the OP's case maybe there was never a converter in the MH as no one ever had a use for it or if there was one it has expired and needs replacement.
2002 Fleetwood Storm 30H on Workhorse P32 chassis 8.1 gas.