I suspect a lot of the time spent looking at the "second screen" is while the first one is showing adverts.
Source: A company I used to work for did a metric buttload of research on this subject.
Then they are only using the handheld (or laptop) screen, and they are not watching the TV
Most television and film content is just unbelievably boring, self-important, and undemanding of the viewer's attention. Frankly, content producers have become more and more disrespectful of the viewer's time.
In very rare cases, I suddenly notice I've lost track of the plot--if that happens a couple times, that's when I know I need to put away my phone/laptop and focus on the show.
It is not obvious which content is actually demanding. For example, the film The Martian was very dense and demanding of attention, while the more recent Ad Astra could be summarized with the single sentence "sad sack mopes around space." Dialog rich comedy is generally the most demanding.
Really? I find that the easiest to just listen to, especially once I know who all the characters are.
Generally it's not important what they're doing, just what they're saying, so I can just listen while doing other things.
Like the shows I relisten to all the time (not watch) while working on the computer are Newsradio, Corner Gas, Larry Sanders, Mr. Show, Red Dwarf, Scrubs, Psych, Arrested Development, Mighty Boosh, Flight of the Conchords, Yes Minister, Mitchell and Webb Look, and a more recent addition, Letterkenny. Pretty much none of that requires my visual attention, except to know that there's a visual gag here or there.
Granted, I usually paid attention the first time I watched it, but not on the rewatch.
We find there are two kinds of movies/TV: stuff that's kinda just relaxing and during which you can browse twitter or whatever, and stuff that's more serious where you can't really multitask without missing important aspects of the show, either because of the filming style or the density of the material or the pace of events or whatever.
The canonical example of the latter is The Wire. More recently, I'd put The Crown or Watchmen in this category. For the former, well, pretty much any traditional network show counts.
However, even in high-attention programming, it's pretty common for one of us to pause the show and check a screen to verify where we saw a given actor before, or look up a related bit of information (e.g., during the Crown, we often check on historical context).
I was watching a movie the other night and there was an uncredited cameo and it's still bugging me because I can't seem to figure out where I've seen him before.