A hand goes down into a crowded space - a drawer, a backpack, a ship's hold - and starts turning things over. You are not tidying; you are looking, and looking fast. Things get pushed aside, and when the hand comes out, nothing sits where it sat before. The mess left behind is part of the word.
From the word’s history
Wiktionary records rummage from Middle English ronage, from Old French arrumage, from arrumer meaning to arrange the cargo in the hold. The word starts on a ship, among crates that have to be shifted about in a tight space.
Wiktionary 記載 rummage 來自中古英語 ronage、古法語 arrumage，動詞 arrumer 的意思是「把貨物安排在船艙裡」。也就是說，這個字是從船上出發的：水手在窄窄的艙底把一箱箱貨搬來搬去。那個在擁擠空間裡撥開東西的動作，一路留到今天的抽屜和背包裡。
Wiktionary (kaikki extract, source_ref kaikki:3f6f69a190036ae4:824216183:27599), rummage verb etymology
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