A wand of enlightenment is immensely useful for identifying noncursed rings and amulets. First make sure you know what your intrinsics are without any equipment (by zapping the wand if necessary) then put on the ring or amulet, zap the wand, and see if any new intrinsics have appeared in the list. Try to test two differently-priced rings that do "nothing" when worn at the same time. You can also tell whether an unidentified gray stone is a luckstone by looking for messages about extra/reduced luck. Another bonus is that enlightenment will let you know whether it is safe to pray.
Wands comprise 4% of all randomly-generated items in the main dungeon, 6% in containers, 5% on the Rogue level, and 8% in Gehennom. There is a 1.5% chance that a randomly-generated wand will be a wand of enlightenment.