Thanks for the update.I wanted to provide an update on this issue for those that might be looking for solutions. The Curt 7-pin to 4-pin adapter with built-in resistors did not fix the issue. I used the "test lights" feature in the trailering app built into the infotainment screen to cycle through all of the lights. Oddly, it illuminated all of the trailer lights except for the running lights. After that test was complete, all of the lights worked and have worked ever since. I'm not ready to call this "problem solved" yet, but I used the trailer all weekend and it worked every time after that test. Maybe the test somehow acquainted the truck's towing computer with the particular load of this trailer? No idea, but so far so good.
When you say the lights worked all weekend, does that include the non-working running lights during the light test?