As I discuss in this question, by far the most popular school of Hindu philosophy is the Vedanta school, which bases its tenets on the doctrines laid out in the Brahma Sutras, a work by the sage Vyasa that summarizes and systematizes the philosophical teachings of the Upanishads. (You can read the Brahma Sutras here.) In any case, in Adhyaya 1 Pada 3 of the Brahma Sutras, Vyasa discuss the issue of who is eligible for Jnana. As I discuss here, he says that low-caste people are not eligible for Jnana, since they don't wear the sacred thread. But before that, he says that the gods are eligible for Jnana.
And that leads him into a discussion of the gods in general, in particular regarding how the Vedas can be eternal if mention the names of gods who do not remain in their positions forever. As I discuss in this answer, the resolution is that the same names recur in different ages. But in his commentary on Adhyaya 1 Pada 3 Sutra 29 of his commentary on the Brahma Sutras, Adi Shankaracharya gives a few other arguments for the Vedas being eternal:
[T]he eternity of the Veda is founded on the absence of the remembrance of an agent only.... The eternity of the word of the Veda has to be assumed for this very reason, that the world with its definite (eternal) species, such as gods and so on, originates from it.--A mantra also ('By means of the sacrifice they followed the trace of speech; they found it dwelling in the rishis,' Rig-veda Samh. X, 71, 3) shows that the speech found (by the rishis) was permanent.--On this point Vedavyâsa also speaks as follows: 'Formerly the great rishis, being allowed to do so by Svayambhû, obtained, through their penance, the Vedas together with the itihâsas, which had been hidden at the end of the yuga.'
I discuss the notion that the Vedas are a blueprint for the creation of the world in my answer here. But my question is about the Rig Vedic verse that Adi Shankaracharya cites, which is verse 3 of Book 10 Hymn 71 of the Rig Veda:
yajñena vācaḥ padavīyamāyan tāmanvavindannṛṣiṣupraviṣṭām |
tāmābhṛtyā vyadadhuḥ purutrā tāṃ saptarebhā abhi saṃ navante ||
With sacrifice the trace of Vāk they foIlowed, and found her harbouring within the Ṛṣis.
They brought her, dealt her forth in many places: seven singers make her tones resound in concert.
As you can see in the Rig Veda Anukramani in my answer here, this verse was heard during Tapasya by Brihaspati, the guru of the gods, and the subject of the hymn is listed as "Jnanam". But my question is, why does Adi Shankaracharya think that this verse proves that the Vedas are eternal?
The verse discusses how Vak, which as I discuss here is a name of Saraswati in her capacity as goddess of speech, was found by the wise as "harbouring within the Rishis." But why does that imply "that the speech found (by the rishis) was permanent"? Is Adi Shankaracharya arguing that the fact that it says the speech was "found" within the rishis as opposed to "composed" by them implies that the Vedas don't have a human author?
Are there any commentaries on Adi Shankaracharya's Brahma Sutra Bhashya that shed light on this?