A good raw apple cider vinegar is full of important minerals like potassium and magnesium. It also reduces to an alkaline ash when processed through digestion. These two facts may explain your cravings. Even though you are early in your fast, you may be experiencing some mineral or electrolyte imbalance. Get a good quality raw vinegar with the mother in it. Bragg's brand is my favorite. Try 1-3 teaspoons in a glass of water or juice two or three times a day. Many people use a little honey or Maple syrup to sweeten the taste. I like to put a few drops of cayenne tincture with mine because it helps the circulation. You might also want to put a little bit of good Sea Salt on your tongue when drinking this, this will assure you are getting sodium and potassium, two essential electrolytes that can become imbalanced when fasting. The pickled beet juice would have both salt and vinegar, so I suspect minerals are what your body wants.
Since fasting makes the body more acid, the alkalizing effect of ACV would also help you. Listen to your body, it sounds pretty smart!