I try to avoid eggs that the yoke is exposed. It tends to cloud the mixture. Most popular pickling juice in my home is beet juice. It gives a sweet flavor that can be offset with onions and pepper. I keep the jar refrigerated.
For smoked eggs, I boil the eggs, peel, then half the yoke. I put the eggs in the smoker with smoldering wood for 30 minutes or so. I then make deviled eggs. I use 1/4 mayo, 3/4 sour cream, mustard powder, and top with smoked paprika. Sometimes I add some shredded sharp cheddar to the yoke mix.