Turn signal circuit and lamps reduced from 12 volts to 5 volts to demo in simulator. Right SPST switches are to show connections to trailer wires.
Top is car tail lights wired direct to trailer tail lights. Not shown is back up lights wired direct to trailer as well.
Transistors are both 40324 silicon n-p-n. If positive ground system change to p-n-p silicon power type with at least 3 ampere current rating.