You can do this if you wire 2 relays with the NC contacts in series with the the wire feeding the lights from the parking lights. Now wire each relay coil with one side to ground and the other side to the brake light for that side of the trailer.
Now whenever the turn signal is on the side marker lights on the side you are turning to will blink.
However when ever you hit the brakes Both side marker lights will go off and remain off as long as the brakes are on. On a longer trailer this might prove to be an advantage giving notice to those who ride your side.
WBCCI 12156 AIR 3144 WACHUNG TAC NJ6
2004 Excursion 4x4
1991 34 ft. Excella +220,000 miles, new laminated flooring, new upholstery, new 3200 lbs axles