I know very little about Vaisheshika, so I'm giving this an interpretation from a Buddhist perspective, just so that you're clear. And just to throw a spanner in the works at the outset, I vaguely remember going through a phase where it seemed like something was holding everything, then it passed.
ideas, feelings, desires and knowledge need a vessel in which they are
contained. And this vessel is what constitutes the eternal, unchanging
It's entirely possible that this refers to the natureless-ness of all phenomena - that nothing of quintessence can be found in all creation, not even awareness itself, which might relate to the eternal, unchanging atman - but I doubt it. In Mayahana and Theravada, this is called Sunyata and is very difficult to talk and write about without sounding like a convoluted academic or a crazy poetic genius, referring to the various forms of Dependent Origination and the Heart Sutra respectively.
It's also possible that it makes reference to a particular region along the journey, let me explain...
...the thing about this stuff is that people generally need an idea of some sort to work towards. That is how some Mahayana schools work. They point to a region just before the thing itself. Their region is called the Pure Lands. The idea about this is that one needs to captivate the self in the same way you might capture the attention of a drunk person who might be wandering near a cliff. Perhaps you'll wave a can of lager at them, and they'll turn away from danger and towards the can of lager - admittedly, this is a very un-Buddhist analogy, but never mind.
This capturing the attention of the aimless wanderer is precisely what the celebrated and prominent Lotus Sutra is about. In a similar sort of way, you might capture the attention of a person lost in delusion with a particular idea about something rather nice like the pure lands. These frilly bits, fleurons and embellishments appeal to the limited yearnings of a conditioned mind. Put simply, sometimes some minds need a little charm to follow. When they get that charm, their curiosity is pulled towards something else, which isn't spoken about all that much.
All in all, the passage sounds a lot like the cries of a subtle sense of self and in the Theravada tradition, they would quickly ferret out that blighter, as in the case of Ven. Khemeka who describes the subtle sense of self like the faint smell of cow dung upon freshly washed clothes.
"Just like a cloth, dirty & stained: Its owners give it over to a
washerman, who scrubs it with salt earth or lye or cow-dung and then
rinses it in clear water. Now even though the cloth is clean &
spotless, it still has a lingering residual scent of salt earth or lye
or cow-dung. The washerman gives it to the owners, the owners put it
away in a scent-infused wicker hamper, and its lingering residual
scent of salt earth, lye, or cow-dung is fully obliterated.
"In the same way, friends, even though a noble disciple has abandoned
the five lower fetters, he still has with regard to the five
clinging-aggregates a lingering residual 'I am' conceit, an 'I am'
desire, an 'I am' obsession. But at a later time he keeps focusing on
the phenomena of arising & passing away with regard to the five
clinging-aggregates: 'Such is form, such its origin, such its
disappearance. Such is feeling... Such is perception... Such are
fabrications... Such is consciousness, such its origin, such its
disappearance.' As he keeps focusing on the arising & passing away of
these five clinging-aggregates, the lingering residual 'I am' conceit,
'I am' desire, 'I am' obsession is fully obliterated."