They should be wired for same function they had as factory equipment. If they are meant to be turn signals then they are too bright for running lights and could be blinding in certain scenarios which may be illegal.
In the US, generally lamps facing rearward (does not necessarily have to physically be on the rear of the vehicle) should be red, while lamps facing to the side, including turn signals or running lights, should be amber.
If they are meant for both functions then there should be separate bulbs and colors.
One thing you could do is put a low ohm resistor in series from the parking light circuit for running lights that aren't excessively bright, going through a normally closed relay. Wire the relay coil to the turn signal circuit for each side. When the other, stock turn signals illuminate it breaks power to the mirror bulbs so they are blinking in the opposite state to the rest of the stock turn signal bulbs.
I'd rather not do that, would make them only turn signals if that was what the design was meant to do. If there is only one bulb you could stuff some amber LEDs in for a lower power running light that's wired separately, into the parking light circuit.