That’s a really good idea! I can imagine two options right off the top of my head.
Disconnect the signal wire and apply a power wire that is connected to the ignition so it turns on as soon as your key is turned or the car is started. This will disable the turn signal.
Connect a resistor with the supply to the ignition power supply, then add a blocking diode on the battery side to prevent the voltage from back feeding the SAM. This would dim the lights for running, and they would brighten when you’re using your turn signals.
…if you’re good with tools and know how to keep the smoke inside the wires is an easy mod…a 3 pin socket will be required and make it fit to the bezel tho…run the hot wire for the running portion of the assembly from the headlight unit…