In the above case, since it talks about avitakka/avicāro it implies second Jhāna.
Sure, but what is vitakka/vicara?
What is interesting, is your pericope "cetayamānassa me pāpiyo, acetayamānassa me seyyo" in the dimension(sphere) of nothingness.
The fact that there is thinking (what we usually call thinking",) at that level goes against the "no thinking" after the first jhana.
We must wonder if the translation of vitakka/vicara as "think/examine" (or "think/ponder") is accurate?
We have seen that the translation of cetayamānassa above as "thinking", was quite undefined.
I might have wrongly interpreted "cetayamānassa me pāpiyo" as "intellectualizing over feeling and perception is bad for me".
"Intellectualizing" does entail "thinking" in the sense that we usually use it. It implies the use of the intellect (mano). Intellectualizing perception and feeling does mean "thinking" over them with mano (mind/intellect). But cetaya is not at this level.
Again, I refer to the extract:
Now, when the monk is percipient of himself here, then from there to there, step by step, he touches the peak of perception. As he remains at the peak of perception,
the thought occurs to him, 'Thinking is bad for me. Not thinking is better for me.
Tassa saññagge ṭhitassa evaṃ hoti: ‘cetayamānassa me pāpiyo, acetayamānassa me seyyo.
If I were to think and will, this perception of mine would cease, and a grosser perception would appear.
Ahañceva kho pana ceteyyaṃ, abhisaṅkhareyyaṃ, imā ca me saññā nirujjheyyuṃ, aññā ca oḷārikā saññā uppajjeyyuṃ
What if I were neither to think nor to will?
yannūnāhaṃ na ceva ceteyyaṃ na ca abhisaṅkhareyyan’ti.
We see that there is the perception of a feeling (ceteyyaṃ;) and an ensuing "will" (a saṅkhāra), if there is conceit (mānassa) over that perception. If there is conceit over that feeling and perception, there is the use of mano, and will (saṅkhāra) (SN 22.47). That is what is bad.
Perception must be rid of the "I"; of the conceit.
This is not vitakka/vicara, though.
We have seen in a previous example that the bikkhu directs (paṇidahi) the citta towards some goal; then withdraws the citta from the goal, and does not think and examine anymore (vitakka/vicara).
The goal in that instance, is a nice attribute (nimitta) of something.
So there is a projection in vitakka/vicara, which does not exist in cetaya.
But is vitakka/vicara a mano process?
Isn't vitakka/vicara at the same level than cetaya (the citta level)? Something that does not need mano; which implies that there is no "thinking" as we usually conceive it.
Vitakka/vicara does project, where cetaya does not. But none of them are at the level of mano (intellect). They are not "thinking" as we conceive it.
Note: cetayamānassa is definitely an interesting term.
In this world with its ..., Māras, ... in this population with its ascetics.... (AN 5.30).
We are all possessed - more or less.
And what, bhikkhu, is inward rottenness? Here someone is immoral, one of evil character, of impure and suspect behaviour, secretive in his acts, no ascetic though claiming to be one, not a celibate though claiming to be one, inwardly rotten, corrupt, depraved. This is called inward rottenness.”