If you're saying what I think you're saying, it's going to be a doozie. I'm having a similar problem with a relatives Nissan Armada where the running lamp and brake lamp are separate signals when on a trailer, the turn signal overrides the brake lamp and causes the flashing. While running lamps stay lit. The issue is the turn signal being the same as the brake, but on the Moho or Nissan Armada it's not. Most of the vehicles setup that way, need a relay for towing harness usually from factory.
For example: I installed a tow package on the wife's Honda Pilot. The wiring harness came with 2 relays I had to put in the hood in their respective place for the wiring to work out back. I was a bit thrown by this but didn't put much thought into it. I bet it had to do with that similar issue.
Get us a pic of the plug and the back of the moho, at least what model to figure out what it has for lighting.
My truck GMC sierra, or Workhorse chassis moho don't have this type of issue I believe because they already use the brake signal for turn signal flash. Pretty simple and goes to a trailer plug no problem most likely. Sorry, I'm just helping you brain storm here.
On the Armada, the great guys at Uhaul that installed their hitch on it, did some Jerry riggin' underneath to get some kind of lights, well no running lights on the trailer. Pissed me off to say the least. They tried to use some sort of Chinese converter and even though I wired it correctly it still doesn't work. I'm left with factory tow harness from Nissan just to get it all to work with their relays as well.