Found this from a thread elsewhere back in 2016... Kinda describes what we've been talking about
I think what is happening is that the truck is using some of the same lamps for turning as running. If this is true, then applying voltage to the driving lamps is backfeeding into the flashing circuit, including your dash directional monitor lamps.
OEM has a single filament bulb for each of the front side lights. One side wires to the Park circuit, the other lead is going to the blink circuit. When Park lights are on, the side filament returns into the otherwise dead blink path and develops a voltage there that is normally not an issue.
When park AND blink is active, the bulb will light only when the other blinking lights do NOT light. Basically, alternating blink. When park is OFF, the sides blink the same time as the others.
Now, when you sub LED's in the system, what little voltage/current got injected into the blink circuit now causes issues, since the new LED blinkers use so little current, therefore the unwanted blink voltage is high, too high.