I looked at the diagram for the blinkers, which in your project the led lights share the blinkers ground. If I assume the diagram to be right, it looks as though the blinkers switches the power and the ground is fixed. In the courtesy light system the ground is switched, meaning it isn't fixed so as not to have a ground all the time, this is what the jam switches do, switch ground. I'm nearly certain th8s is why the courtesy lights come on when you close the door. My best suggestion at this point, which is where I would start if it were my truck, is to look at the courtesy lamp circuit, look at the 4 courtesy lamps in the middle of the second diagram and imagine the running board leds there as well. This is the longer way around, but it would eliminate potential issues, so if the led lights have 2 wires, one being + and one being -, I would then connect the led + to the orange at the splice above the lights on the diagram, then take the led - and connect it to white, at the splice below the courtesy lamps. I suspect that would work as intended.