How do I analyze this sentence from John Dyson's "Don't Look Down"?

This is almost certainly an example of a compound subject with the coordinator or deleted for dramatic (staccato) effect:

The cable heaping on the roof, [or] even a vibration from the men inside, could nudge the 2.4-ton cage into free fall.

A ... or even B ... could do X. ==> A, even B, could do X.

The comma after 'inside' forces the compound subject analysis.

Your analysis of the Dagger sentence is on target, but the Cable sentence is quite different in structure. The two comma-separated phrases that begin the Cable sentence are grammatical subjects for the predicate that follows, while the subject of the Dagger sentence is he, modified as you note by the preceding expression.

Having two subjects thus share a single predicate is a form of zeugma. (It is of Type 3 per the typology in the linked Wikipedia page.)

The mental image I have from this is of a cage (a mine shaft cage) being lowered and sticking in one position; the cable is still paid out from above and heaps on the cage top because the operator does not know the cage has stuck; in consequence, the situation of the occupants is dangerous because even their own small movement (the vibration) might free the cage, leading to its perilous and uncontrolled descent.

{Because of the circumstance of} the cable heaping {and perhaps continuing to heap} on the roof, even a vibration {any small movement} from the men inside could nudge the 2.4-ton cage into free fall.