Hold on to the sentence hiding inside the word: will I, nill I — I am willing, I am not willing, and it makes no difference either way. What that sentence really says is that nobody's preference is being consulted. Point that at a person and you get the older meaning: the crowd, the rule or the flood moves them and their wishes count for nothing. Point it at a job of work instead, and the same absence of choosing shows up as mess: if nobody is deciding what goes where, boxes land in the doorway and names land on the list. One picture, two directions — no choice being made about you, or no choice being made at all.
From the word’s history
The packet's Wiktionary entry spells it out: willy-nilly is will I, nill I, with nill the old verb meaning to be unwilling, both verbs in the subjunctive, and the ee sound of I reflecting pronunciation before the Great Vowel Shift. Related forms will he, nill he and will ye, nill ye are recorded with the same meaning.
packet 裡的 Wiktionary 講得很清楚：willy-nilly 就是 will I, nill I 縮成的，nill 是古英文「不願意」的動詞；當時的 I 還唸成 ee，所以縮起來會是 willy-nilly。同樣結構還有 will he, nill he 和 will ye, nill ye，意思一樣。
Wiktionary, "willy-nilly"
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