Laura -- I checked a number of the pickled egg recipes to see if I could get some clues to answer your question. Most of them called for refrigerating the pickled eggs. Perhaps your local county extension office can advise you about best processing method and time, or perhaps it might be covered in a database here.

Pickled Eggs

12-16 hard boiled eggs, shells removed
2 c. white vinegar
2 T. sugar
1 t. salt
1 T. mixed pickling spices
1-3 med. onions, cut into rings
1 whole clove garlic

Arrange whole eggs and onion rings in alternating layers in a large glass jar with tight-fitting lid. A whole clove of garlic may be dropped into the jar. Vinegar is measured into saucepan; add salt, sugar and pickling spices. Mixture is simmered 10 minutes after reaching boiling point. Hot pickling mixture is poured into jar tocompletely cover egg and onion rings. Seal jar.
Refrigerate for 2 days before eating. Store in refrigerator.