Yes, that's the harness I was talking about - there is no connector to the battery, just a wire lead with a "eye" terminal (you can cut this off & use what ever size you need) - the factory (+) battery wire has a 10mm nut on it I believe - you can just take this off & put the "eye" terminal underneath it & tighten back down - you don't need any extra terminals on the battery itself to do this install.
I did the independant fog lamp mod - instead of cutting the wire, I stripped off the insulation & wrapped a wire around it - then I grounded it behind the glove box - never had any issues with the fog lights, going about 3 years now (I had to replace both ballasts due to poor mounting location on my part & getting water intrusion in them & cooked them nicely - 2 new ballasts & relocated mounting position & all has been well
) - I noticed in another post you did you mentioned that the fog light indicator on the dash dims out when you shut the fogs off - mine does this as well ever since the HID install - I figured its just the residual charge from the ballasts dissapating & never really think about it anymore - no issues with it (fog lights are controlled by grounding thru the DRL module) So I don't believe that this mod should be affecting the operation of the HID's
If all else fails, you may have to try another brand of HID kit - I have heard of some people up my way using DDM HID"s & needing the relay harness for stand alone headlamps (non-DRL) - the price is right but sometimes the cheaper kits are more sensitive to voltage supply & need some help - the brand I have is Litech (I'm not sure if its available everywhere) - I have 35W 6000K Low beams & 35W 3000K Fog lights (both without use of relay harness) - Hope this helps out & good luck!