Scrub potatoes and place in large pot. Fill three-quarters of the way with lukewarm water, add salt and bring to a boil. Cook until potatoes are fork-tender, about 10 minutes. Drain and let cool just long enough to be able to handle. Peel skins off potatoes while still warm. They should come off easily. Cut potatoes into large bite-sized chunks and set aside.
Meanwhile, fill medium saucepan pan two-thirds of the way with water and bring to a boil over medium-high. Carefully lower eggs into pan. Cook 10 minutes over a gentle boil. Prepare a bowl of ice water for eggs. After cooking, immediately submerge eggs into ice water and let sit at least 2 minutes. Peel and dice eggs.
Using a mesh strainer and a bowl, drain pickles and all the good stuff at the bottom of the jar. Separate peppercorns, pimientos and other seasonings from pickles and set aside. Dice 1 cup pickles (roughly 2 whole pickles), returning remaining pickles and juice to the jar, if wanted.
In large bowl, toss potatoes, eggs, pickles, olives and onion.
In small bowl, mix remaining ingredients until well combined. Add mayonnaise mixture to potato mixture, adding more mayo, vinegar, salt or pepper to taste. Garnish with paprika.