Helen, according to the NCHFP (National Center for Home Food Preservation, where you can always trust their tested recipes and advice) :

There are no home canning directions for pickled eggs. All pickled egg recipes are for storage in the refrigerator. Pickled eggs should never be at room temperature except for serving time, when they should be limited to no more than 2 hours in the temperature danger zone of 40 to 140 degrees F.

Caution: Home pickled eggs stored at room temperature have caused botulism

Morz was quicker than I was. Here is a link to all the info on them.

http://nchfp.uga.edu/how/can_06/pickled_eggs.html

There are sources on the web that are fully trustworthy and NCHFP is the primary one. But there are hundreds of web sources that are far from safe to use. Knowing which websites and which books are safe is very important when home canning foods.

Dave

Thank you Dave. I know I can trust what you have to say. I guess I will continue to just keep the eggs in the fridge.