After some research I found a few names used for this in the industry. It is called an "Eye bar", a "Shatner light" or, "Kirk light". Apparently It originated in classic black and white films. I cant verify this but it seems it was either first done or made popular by the 1931 Dracula film (image attached) which at least 3 black and white remakes all used the same Eye bar lighting. It then started to be used in other Genres and films including Star Trek the original series where it was used extensively for Kirk (images attached), thus the name Kirk/Shatner light. It was also used in the Harry Potter movies at least once.

As mentioned in the OP it was so common it was used as a running joke in the Addam's Family films anytime Morticia was in a shot (see the original post for an example).

@ringo