This is a guess, but I think I figured out where this is from, and it’s goofy as heck. There’s a line from Book IX of the analects, I’m looking at https://en.wikisource.org/wiki/The_Analects/Book_IX. for reference. The specific line is “子在川上曰、逝者如斯夫、不舍晝夜。”, which that particular site translates as “The Master standing by a stream, said, “It passes on just like this, not ceasing day or night!””.
Breaking this down left to right, 子 in this context just refers to Confucius, and 在川 means “Located at or in reference to a river”. (I believe 上 is part of this structure, since it makes less sense attached to the verb, so it’s technically above the river, e.g. on an embankment of some kind.) Classical Chinese is very, very generally SVO, and it’s usually a good first guess to assume that a novel compound is topic-comment with the topic on the left, so we can conclude that Confucius is the topic “down by the river” is referring to. (Please note that, like most Classical Chinese grammar, both the SVO and topic-comment duo are more polite suggestions than hard rules, depending on the syntax to consistently work this way will ruin your day.)
So, what’s this dude doing down by the river? 曰 generally just means to speak, so it informs us that everything which comes after this is a direct quotation. (Like a lot of classical chinese passages this doesn’t deign to use quotation marks, because it was structurally obvious from context.)
I’m going to pause for a moment and skip to the very end of the quote, because this wouldn’t be an effective discussion of Classical Chinese grammar if I actually took it in order. The last bit, “不舍晝夜,” basically means “doesn’t stop, day or night”. 晝 means daytime or daylight, 夜 means evening, and 不 negates whatever comes after it, which usually means discard in Mandarin, but can more generally mean “to cease” in Classical Chinese.
So blah blah guy, blah blah river, something, something, can’t stop won’t stop 24/7 party philosopher. That leaves us with the middle section, 逝者如斯夫, which is where this gets goofy and entertains me to the point that writing a rambling post about Classical Chinese is pseudo-justified. 如斯夫’s job is to connect what’s on its left to what’s on its right, in this case it explicitly establishes that 逝者 is the thing that doesn’t stop day or night. (You can think of it as basically meaning ‘it’s like this’.)
So that leaves 逝者. 逝 can basically mean “in the past,” nouns or abstract concepts that used to exist, but don’t now. In this context 者 is modifying 逝 as a nominalizer, so “逝者” can be thought of as “things that have passed”- literally, undefined nouns that used to exist but don’t anymore.
But, here’s the kicker: remember how I said that you shouldn’t rely on every construction being topic-comment, because Classical Chinese grammar is more of a polite suggestion than a hard and fast rule? 者 isn’t always a nominalizing suffix, it can also mean “Person”. If you were to look at this funny, you might conclude that 逝者 is a comment-topic sentence, where the comment has been moved to the left to add emphasis, and instead of meaning “stuff that used to exist,” it literally means “a guy that used to exist,” e.g. a dead person.
Thus, if you pass this through several iterations of bad translation and poetic license, “Time is like a river, passing day and night” could be badly mangled into “If you sit at a river day and night and never leave, a dead person will eventually appear”.
So I have no clue if that’s actually where this comes from, but it makes a heck of a lot of sense to me. (Also, I’m a Japan guy, not a China guy, and I’ve never heard anything that even comes close to this from the Japanese side.)