Combine both vinegars, water, sugar & salt into small saucepan over medium-high heat. Simmer & stir until hot and sugar is dissolved.
Remove from heat, stir in tumeric.
Put peeled eggs in an appropriate sized mason jar or other glass container.
Pour vinegar mixture over eggs in jar.
Cover & refrigerate. The tumeric will settle to the bottom of the jar, so give the jar a swirl, roll or shake a couple times a day. This also helps move the eggs around insuring that everything pickles.
Wait at least 24 hours to eat. I prefer the taste after day 3.
My preferred cooking method for hard boiled eggs: Bring water to a gentle boil, add eggs, cook for 13-14 minutes. Immediately chill in cold water. I find hard boiled eggs are easiest to peel after chilling in the fridge for a few hours.