Who is the actor with the most screen time in a movie who was credited under a generic character description rather than a name or nickname? [closed]

The Road had several such characters, but this falls outside the scope of your question.

Viggo Mortensen and Kodi Smit-McPhee were both in almost all of the 111 minutes of The Road. They were credited as "Man" and "Boy," respectively. Mortensen probably had slightly more screen time than Smit-McPhee. They were neither the only man or boy in the film and there was a named character: Ely, played by Robert Duvall. Charlize Theron as "Woman" had much less screen time.

There are almost certainly similar lead characters with generic character names. After all, "The Scarecrow," "The Tin Man," and the "Cowardly Lion" are all generic names. While this addresses your question to the letter, it does not answer the spirit of your question, since you are looking for extras and not leads with major roles.

Your question is not really answerable without a complete survey of all movies.

One would have to review almost every movie ever made to give you a definitive answer. There are a few roles that come to mind, such as Vic Tablian as "Monkey Man" in Raiders of the Lost Ark. That character appeared in multiple scenes during the Cairo sequences that amounted to fairly significant amount of screen time (Tablian also played the named character Barranca in the movie's opening). However, the best you're going to get is someone's best estimation.

I suspect your answer is probably a villain's henchman in some movie or other. The good guys usually all get names, but often there are secondary villain characters that do not, even though they appear in a large number of scenes. Alternatively it might be a character credited by title only, such as Henry Fonda as "The President" in Fail Safe.

As the only character in the entire movie, in almost every single shot and yet never named - credited only as "Our Man" - it has to be Robert Redford in All is Lost (2013)

Honourable mention must also go to Clint Eastwood for playing 'the man with no name' in three different movies; though I'm not even going to guess at the total screen time for the purposes of this exercise.

I was going to question this in a comment, but I think it would fit here…

Why do you insist this must be an 'extra' (very non-PC name these days, btw, the term is Supporting Artist;) when there are world-famous actors who have done entire movies without a character name?
You'd also be very hard pressed to tell the difference between a Day Player and a Supporting Artist based only on the movie credits scrolling at the end - you have to ignore IMDB for this, as some people put their own credits in^[1]. There are also cases of nameless characters credited on the movie itself but not in IMDB; it can depend on who was employed to fill in the credits on there.
There's also additional confusion in deciding this, as a minor character playing right through a movie as 'henchman' etc might be a Day Player the days he gets lines, yet an SA the rest of the time he's there. This can be very much an individual contract negotiation.

^[1] I could write an entire page on why I think this is despicable… but not here.