By ``running lights'', do you mean your dashboard lights? I mean, I can't imagine why running lights would be in that connector,

I think he just means that when he turn on his running lights (called parking lights in the US) or when he turns on his headlights, then the following things happen:

- The dashboard lights also come on.
- The wire we're talking about goes +12v.

This all sounds kosher except the fuse blowing.