Hey Thumper -
I know the feeling - I just took one of my kids there yesterday, and he told me he "loves In-N-Out more than any other fast food"...
The kraft thousand island seems kind of similar, but I do know there's pickles in the sauce, and I have heard that another ingredient is lard. But, the second is only what I've heard - don't know that as fact.
Have you seen all the branded merchandise they have? You can even get one of their signature red aprons with the big pin on the back(!) In-N-Out Burger Company Store