I can only speak from my understanding of the suttas.
According to Anapada sutta, in third jhana one attains: Sampajañña - commonly translated as "clear knowing", "clear understanding", or "constant thorough understanding of impermanence"
"Furthermore, with the fading away of rapture, he entered and remained in the third jhana, where he meditated with equanimity, mindful and aware, personally experiencing the bliss of which the noble ones declare, ‘Equanimous and mindful, one meditates in bliss.’
Puna caparaṃ, bhikkhave, sāriputto pītiyā ca virāgā upekkhako ca viharati sato ca sampajāno
, sukhañca kāyena paṭisaṃvedeti. Yaṃ taṃ ariyā ācikkhanti: ‘upekkhako satimā sukhavihārī’ti tatiyaṃ jhānaṃ upasampajja viharati.
"And he distinguished the phenomena in the third jhana one by one: bliss and mindfulness and awareness and unification of mind; contact, feeling, perception, intention, mind, enthusiasm, decision, energy, mindfulness, equanimity, and attention. "
Ye ca tatiye jhāne dhammā—sukhañca sati ca sampajañña
ñca cittekaggatā ca, phasso vedanā saññā cetanā cittaṃ chando adhimokkho vīriyaṃ sati upekkhā manasikāro—
Wikipedia article on Sampajañña - https://en.wikipedia.org/wiki/Sampaja%C3%B1%C3%B1a
This quality is not present in the previous jhanas, and I'm guessing not in access concentration either. If you look at the suttas involving the third noble truth "Impermanence" is always the first characteristic to be seen and understood.
"The perceptions of impermanence, not-self, ugliness, drawbacks, giving up, fading away, cessation, dissatisfaction with the whole world, non-desire for all conditions, and mindfulness of breathing." -AN10.60
or the last tetrad of anapanasati, first step: "" He trains himself, 'I will breathe in focusing on impermenence.' He trains himself, 'I will breathe out focusing on impermenence.' -MN 118