What do these lines from Ulysses mean exactly? What is a sinking star? How does the simile work in the first line? This summary calls the phrase ambiguous.
To follow knowledge like a sinking star,
Beyond the utmost bound of human thought.
The main ambiguity, for me, likes in that this could be either a positive or negative reference for seeking knowledge.
A "sinking star" also has two possible meanings, so there's more ambiguity.
A falling star/meteor/shooting star is a brief flash, then disappears. Seeking it is pretty much guaranteed to be fruitless.
A star that sinks below the horizon is also something that can be followed, and this one suggests excitement and adventure and huge rewards. Think "second star on the left, and carry on til morning!", or the Wise Men's following of the Star in the East. But ambiguously, it also suggests fruitlessness: you can go around the earth any number of times and you'll never reach that star!
Either way, it seems to say that the pursuit of all knowledge is ultimately unattainable, for "Beyond the utmost bound of human thought" is somewhere that cannot ever be reached by a human, a boundary forever receding.
But, is the quest to push back that boundary a noble and worthy one, or a naïve and foolish one? The quote leaves this unclear, and therein lies the ambiguity.
It refers to a star falling below the horizon, still present but which cannot be followed in plain sight.
Quite how one follows knowledge when it is beyond being thought about is rather more obscure. It's why literary criticism is off-topic, and I'm not going to attempt to analyse Joyce. Or even Tennyson.