I almost always eat the pickle in between halves. Slightly more problematic if the sandwich is cut in thirds, but the principal is the same: In the middle of the meal, starting and ending with the sandwich. If I try, I can usually finish the chips/fries before the last bite of sandwich, or not eat the last chips at all. I'm not a fanatic about it, but use this paradigm more often than not.
A luncheon group of five fen had no agreement on pickle management, and clearly this is a matter of, um, taste. So I throw the field open for discussion.