In instant pot: place 1 cup water and trivet inside instant pot along with eggs. Cook on high pressure for 5 minutes and let nature release for 5 minutes. Place eggs in bowl of cold water and let cool for 5 minutes before peeling.
On stove: place eggs in pot of water and bring to a rolling boil. Take off heat and let sit, covered, for 12 minutes. Remove eggs to ice bath for 5 minutes before peeling.
Remove yolks from eggs and mash them thoroughly in separate bowl.
Roughly chop eggs in a small bowl.
Add pickle relish, mustard, and mayonnaise. Stir thoroughly. Add additional mayo if needed to achieve desired texture.
Add salt to taste.
Eat on a bagel, sandwich, or by itself with saltines.