You could use a magnetic contact (single-leaf gate: magnet on leaf, sensor on opposite from hinges side - double-leaf gate: magnet on one leaf, sensor on other leaf with cable running on/through leaf), a 12 VDC power supply and a 12 VDC changeover relay.
Run power supply (+) through magnetic contact (gate closed: contact closed / gate open: contact open) to appropriate trigger terminal of relay and (-) directly to other trigger terminal. Run the phase, through relay (enter at COM, exit at NC), to lights and neutral directly to lights.
Use a magnetic contact suitable for outside installation ("heavy-duty"), cable suitable for outside installation and, in case of double-leaf gate, for repeated bending, and that DC power supply is protected from weather but has "breathing" space to keep it cool.
This setup is totally independent from the automation.
You may want to use a delay-off timer after the relay (to keep lights on for some extra time after gate closes) and/or a light sensor (crepuscular sensor) so that lights stay off during the day.
Remarks: 1) If power supply is off, lights will stay on. 2) You can also use this setup to create a "gate left open for too long" system by connecting a delay-on timer after the changeover relay (I prefer to use the relay output to light a warning lamp, so that I know the gate isn't closed, and the delay-on timer output to sound a buzzer, so that I know it's been in this state for too long).
Run power supply (+) through magnetic contact (gate closed: contact closed / gate open: contact open) to appropriate trigger terminal of relay and (-) directly to other trigger terminal. Run the phase, through relay (enter at COM, exit at NC), to lights and neutral directly to lights.
Use a magnetic contact suitable for outside installation ("heavy-duty"), cable suitable for outside installation and, in case of double-leaf gate, for repeated bending, and that DC power supply is protected from weather but has "breathing" space to keep it cool.
This setup is totally independent from the automation.
You may want to use a delay-off timer after the relay (to keep lights on for some extra time after gate closes) and/or a light sensor (crepuscular sensor) so that lights stay off during the day.
Remarks: 1) If power supply is off, lights will stay on. 2) You can also use this setup to create a "gate left open for too long" system by connecting a delay-on timer after the changeover relay (I prefer to use the relay output to light a warning lamp, so that I know the gate isn't closed, and the delay-on timer output to sound a buzzer, so that I know it's been in this state for too long).