Criticism of atman and the vessel analogy

I'm not familiar with Vaisheshika, but I've heard of this:

And (a permanent soul has to be admitted) because of the fact of remembrance (ie., memory).
Hindu scripture Brahma-Sutra 2.2.25

This can be easily refuted. Anyone who injures his brain or suffers from dementia or Alzheimer's, will have memory loss or altered personality.

In Buddhism, mind is considered to be changing from moment to moment and it's not permanent, by any measure.

But what's called 'mind,' 'intellect,' or 'consciousness' by day and by night arises as one thing and ceases as another. Just as a monkey, swinging through a forest wilderness, grabs a branch. Letting go of it, it grabs another branch. Letting go of that, it grabs another one. Letting go of that, it grabs another one. In the same way, what's called 'mind,' 'intellect,' or 'consciousness' by day and by night arises as one thing and ceases as another.
SN 12.61

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 atman.

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."
Khemaka Sutta

The Buddha deals with eternalist views in DN1. For example, eternalist views based on recollection of past lives are introduced here:

DN1:1.33.2: It’s when some ascetic or brahmin—by dint of keen, resolute, committed, and diligent effort, and right focus—experiences an immersion of the heart of such a kind that they recollect their many kinds of past lives.

However, for this post, we are more interested in eternalist views that are based on logic. In this case, the Buddha mentions the fourth eternalist view:

DN1:1.34.2: It’s when some ascetic or brahmin relies on logic and inquiry. They speak of what they have worked out by logic, following a line of inquiry, expressing their own perspective:
DN1:1.34.3: ‘The self and the cosmos are eternal, barren, steady as a mountain peak, standing firm like a pillar.
DN1:1.34.4: They remain the same for all eternity, while these sentient beings wander and transmigrate and pass away and rearise.’
DN1:1.34.5: This is the fourth ground on which some ascetics and brahmins rely to assert that the self and the cosmos are eternal.
DN1:1.35.1: These are the four grounds on which those ascetics and brahmins assert that the self and the cosmos are eternal.

The Buddha does not actually present a logical argument against such views. Instead, he simply asserts that they lead to rebirth and that there is no need for such views.

DN1:1.36.1: The Realized One understands this:
DN1:1.36.2: ‘If you hold on to and attach to these grounds for views it leads to such and such a destiny in the next life.’
DN1:1.36.3: He understands this, and what goes beyond this. And since he does not misapprehend that understanding, he has realized extinguishment within himself.
DN1:1.36.4: Having truly understood the origin, ending, gratification, drawback, and escape from feelings, the Realized One is freed through not grasping.

Briefly, the Buddha simply asserts here that there is no need to grasp at eternalism on the Noble Eightfold Path. Such grasping will not lead to the end of suffering.