You can put a jumper between pins 4 (12 volts) and 3 (running lights) on your trailer cord to check your running lights. If they work with that jumper then your trailer wiring is good. If they don’t work with the jumper then there is where you begin troubleshooting.
If they work with the jumper then the problem is with your truck. Get a 7 pin tester to plug into your truck connector. My truck had a connector in the bed and another at the bumper. When I plugged into the in-bed connector one of the pins would not always conduct. (Been a few years but I think it was the running lights) I could push and wiggle the connector and the lights would come on. The bumper connector always worked fine. I ended up replacing the in-bed connector as I preferred to plug in there.
https://www.amazon.com/Vehicle-Trail...11324560&psc=1