Place zucchini and onions into a large bowl, cover with water, and stir in salt until dissolved. Let the vegetables soak in the salted water for at least 2 hours; drain and transfer to a large heatproof bowl.
Bring sugar, vinegar, celery seed, turmeric, mustard, and mustard seeds to a boil in a saucepan; pour the mixture over the zucchini and onions. Let the mixture stand for at least 2 more hours. Return zucchini, onions, and pickling liquid with spices to a large pot and bring to a boil. Boil for 3 minutes.
While vegetables are soaking in pickling liquid, sterilize jars and lids in boiling water for at least 5 minutes. Pack the zucchini and onion into the hot, sterilized jars, filling the jars to within 1/4 inch of the top with pickling liquid. Run a knife or a thin spatula around the insides of the jars after they have been filled to remove any air bubbles. Wipe the rims of the jars with a moist paper towel to remove any food residue. Top with lids and screw on rings.
Place a rack in the bottom of a large stockpot and fill halfway with water. Bring to a boil and lower jars into the boiling water using a holder. Leave a 2-inch space between the jars. Pour in more boiling water if necessary to bring the water level to at least 1 inch above the tops of the jars. Bring the water to a rolling boil, cover the pot, and process for 10 minutes.
Remove the jars from the stockpot and place onto a cloth-covered or wood surface, several inches apart, until cool. Once cool, press the top of each lid with a finger, ensuring that the seal is tight (lid does not move up or down at all). Store in a cool, dark area, and wait at least 24 hours before opening.