Please refer to the Starch Content of Foods section.
I do not believe black pepper has any starch; I have never reacted to it.
Cooked broccoli has very tiny amounts of available starch and most of us never react to this. Carrots and cauliflower DO have too much starch, however; this is reasonable information with which to "calibrate" Your testing technique. I don't know about zucchini--some varieties are more starchy than others, it seems. Not sure about GAPS diet, but I did not eliminate nightshades (except potato and never consumed any tobacco).
I use a 1% iodine solution called "Atomidine" or "Atomic Iodine;" it can (atypically) be used as a supplement.