Well Gang,
This kind of scenario where simple running lights get sooooooooooooo dam... complicated because they're tied in with the TIPM. And when a $1.25 diode or resistor fails, or, even say a $100 micro processor fails in that TIPM, you, as the end user, get to pay whatever a dealer wants to charge, in this case a $1,000 JUST to get the simply running lights working again and power up the trailer running lights. It was soooooooooooo simple in the old days. EVERYTHING WORKED, and it worked EVERY SINGLE TIME, unless there was a bad ground or a blown bulb.
The OP, and anyone else that has a 7-pin plug installed from the factory, should be able to use those without fail. As for plugging in the 7-pin plug from a trailer to the 7-pin receptacle on the truck WHILE the truck is running or ignition is ON, well, we have a new-to-us '21 Ram 1500 Crew Cab Laramie 4x4 Ecodiesel and I've plugged the boat trailer into that 7-pin receptacle on the truck while the truck is running, several times and absolutely nothing has happened to the trucks electrical system or the TIPM. Each time, the trailers running lights immediately light up when the plug is inserted. Those systems, TIPM and anything else involved should, I say SHOULD be able to take a jolt of a load, such as plugging in a trailer WITHOUT doing any damage to any portion of th electrical system.
Ram can't even possibly think that every single truck owner, for every single truck they sell, will MAKE SURE that the truck is COMPLETELY OFF BEFORE plugging in any trailer(s). If damage to the TIPM would take place every single time a Ram owner plugged in a 7-pin connector to the trucks plug while it was running or ON, all Ram chassis RV's, trucks, commercial trucks, towing trucks all over the planet would be blowing the TIPM and Ram would be inundated with phone calls/complaints by the hundreds of thousands.
Not that this would help the OP at present, or anyone else, I finally built my new little toy/tool that really helps with both the new wiring of a trailer/toad (vehicle towed behind an RV) and the occasional testing of existing wiring of all trailers and toads with a 7-pin connector. It's simply a box with a 12V battery in it and it's wired through a set of toggle switches to the 7-pin female (truck/RV side) female connector. When I want to check either of the vehicles we tow, the Ram or, our '15 Jeep JKUR Rubicon, or, our Bennington Tri-toon boat trailer's lights, I simply carry the box, which is nothing but a small Harbor Freight Ammo box, over to the receptacle for any of those three and plug in the box to it. Then, I begin flipping the switches, one by one, to send power to what ever circuit I want to test, running, right turn, left turn, Brakes and even 12V power if it's equipped. It just makes insuring that all trailer/toad lights are working correctly WITHOUT using any of the vehicles as power to test the systems.
Scott