Identifying live and neutral wire of an old lamp
Unscrew the bulbs and see which wire is connected to the side-contact that contacts the thread of the bulb using a continuity tester. That one is the wire you want to be the neutral. 

That way the live contact is buried deep within the socket and harder to reach by inquisitive fingers.

The dark brown looks to be the ground connection. Check that it has continuity to the metal housing to verify.