I cannot fathom any current B738 driver sitting with his thumb on the pickle switch for that length of time
Very easy to fathom.
The pilot presses the switch, and leaves it pressed, knowing that he is going to have to leave it pressed for a good 5 seconds or so.
But, approaching the 5 second mark, he gets distracted. This was about the time the aircraft was levelled off, so the need to manage the flight path would have provided several challenges that would easily be enough to distract a tired pilot.
Was there a radio exchange at around this time? If so, that could also have served as the distraction.
Being distracted, his thumb just remains on the switch ...
I bet Boeing will modify the trim logic so that the trim can only be run for a maximum of a few seconds at a time.