There's a few things that would cause your problem. That circuit is grounded through the light fixture for starters. Check with a test lamp to the connection inside the socket where the bulb makes a contact and see if you have power there. The buttons that make the connection sometimes get stuck down and don't make a connection. Secondly trace the wire for that circuit back and test the circuit at the connection in the plug. The running lights are connected together to a common feed so the problem is either in the wire to the effected light or the socket itself.
It may be helpful if you add to your avatar area the bike we are talking about here too instead of just a "68".