The "anointing" of JWs has always interested me and puzzled me , really. Unlike most Christian religions , where profession and personal testimony of such an experience is encouraged and even expected , in JW circles , it is roundly discouraged - even mocked by the leadership ( and the source of much negative gossip in the congregation ). An "anointed" elder in a neighbouring congregation was unofficially banned from giving talks in our Kingdom Hall because he tended to "go on about it" in his talks and comments.
The whole JW ethos is to supposedly to build a strong relationship with God ( which in reality is a strong affiliation and devotion to the Org ) but within limitations. Its an odd concept- and I would imagine , pretty unique. I'm guessing that emotions are involved - perhaps some kind of mechanism similar to that which Derren Brown describes in his video is going on and people associate the trigger event with being anointed.