I get a big pickle jar--1/2 gallon?-- and fill it with peeled boiled eggs--3 dozen or so. I add seasoning, then fill to the brim with straight apple cider vinegar, cap and set in the fridge. In 3 days, I take it out and drain all the liquid. At this time, the eggs have neutralized all the acid from the vinegar. I refill the jar with fresh vinegar and more seasoning. This gives a bit of pickled flavor, but if you really want em to keep and have a pickled "bite", then drain them again after another 3 days, the liquid will also be neutralized, and refill with fresh straight vinegar. I add beet juice to the vinegar simply to tell how far the pickling has penetrated the eggs.
The first pickle solution will only penetrate part of the egg white. The second will get into they yolk, and the third will give complete penetration. Otherwise, the beet juice doesnt change the flavor as far as I know, but with the peppers and such that I put in,,,,,,,,,,,,