Verify that the term 'Third Man Factor' descends from Eliot's poem (and the Shackleton 'four, not three' wording) against primary sources

claim-third-man-factor-name-descends-from-eliot-waste-land makes a mildly surprising, load-bearing historical/etymological claim: that the scientific and popular term "Third Man Factor" descends specifically from T.S. Eliot's The Waste Land (l. 360) rather than directly from Ernest Shackleton. Under the sources.md floor, a surprising and load-bearing historical claim should escalate from Tier 3–4 toward Tier 1–2. The Eliot footnote is quoted verbatim from an annotated-text resource (defensible), but the derivation of the term itself currently leans on a Wikipedia-tier etymology.

What to confirm:

1. Shackleton primary: that South (1919) actually contains "it seemed to me often that we were four, not three" (or the exact wording), locating it in the text of the Ross Sea / South Georgia crossing.
2. Term provenance: who first attached "Third Man" / "Third Man Factor" to the feeling-of-a-presence phenomenon, and whether that coinage explicitly invokes Eliot's poem. John Geiger's book The Third Man Factor (2009) is the obvious popularizer to check as the naming node — does it credit Eliot, Shackleton, or both?
3. Whether any peer-reviewed clinical literature uses "Third Man Factor" as a term of art, or whether it is strictly a popular-science label layered onto the clinical "feeling of a presence."

Why it matters: the note's whole cross-domain payoff (neuroscience ← poetry ← exploration memoir) depends on the naming chain being real and not a tidy retrospective just-so story. Until checked, the note stays seedling.