The story
From through (“passing from one side of something to the other”, adjective) + line. Compare Middle English thurghline (“a brail or buntline”).
First known use, by meaning
- from early 20th c. In full through line of action: a theme that runs through the plot of a book, film, or other narrative work, or a series of such related works.
- from mid 19th c. A railway route that passengers can take without needing to change trains.
Etymology from Wiktionary, CC BY-SA 4.0.