Picture someone standing at the side of the action with a watch in their hand. They are not running the race and not doing the work; their one job is to hold the time for everybody else. Keeper is the same element as in goalkeeper and : the one who looks after a thing. A timekeeper looks after time. From that picture the word points two ways. One way is the person or thing that holds the time for others: the official at the finish line, the clerk with the hours, the drummer holding the beat. The other way is a judgement — how well a person or a watch keeps to the time — and that way always needs a word like good or bad in front of it.
From the word’s history
Wiktionary gives the word simply as time + keeper. Keeper is the same element as in goalkeeper and shopkeeper: the one who looks after something. So the whole word is the one who looks after the time.
Wiktionary 直接把這個字拆成 time + keeper。keeper 跟 goalkeeper、shopkeeper 的 keeper 一樣，都是「看管某樣東西的人」，所以整個字就是「看管時間的人」。
Wiktionary entry for timekeeper, packet etymology_text 'From time + keeper' (source_ref kaikki:3f6f69a190036ae4:998189876)
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