Wash and trim the zucchini, then slice them lengthwise into 1/16-inch-thick slices on a mandoline. (You could slice them crosswise, too, but Zuni's are lengthwise.)
Slice the onion very thinly as well.
Combine the zucchini and onions in a large but shallow non-reactive bowl or casserole dish, add the salt, and toss to distribute. Add a few ice cubes and cold water to cover, then stir to dissolve the salt.
After about 1 hour, taste and feel a piece of zucchini—it should be slightly softened. Drain and pat dry. Meanwhile, combine the vinegar, sugar, dry mustard, mustard seeds, and turmeric in a small saucepan and simmer for 3 minutes. Set aside until just warm to the touch. If the brine is too hot, it will cook the vegetables and make the pickles soft instead of crisp.
Transfer the zucchini and onion pieces to three two-cup canning vessels (or the equivalent) and pour over the cooled brine. Seal tightly and refrigerate for at least a day before serving to allow the flavours to mellow and permeate the zucchini. They'll last for a week in the fridge.