Single Perfect Tear
This is sometimes referred to as the “Single Emo Tear of Manly Angst” (which originated on TWOP) or variations thereof.
The term also spread to the writers' room, as evidenced by this quote from Sera Gamble:
Abandon All Hope... was the first time I actually cried watching a director’s cut. At first I thought maybe I was just having one of those days, but I checked in with the other writers… I don’t want to incriminate anybody, so I will just say that one or more male producers also shed what we like to refer to as A Single Perfect Man-Tear.
It is unknown if this ability is in anyway related to Jensen's Wonky Eye.