Where is careless attention (ayonisomanasikāro) in Dependent Origination?

I think the first link ignorance and the eight link Thanha (craving) is the result of Ayoniso Manasikara.

Based in MN 19, I say inappropriate attention occurs at nama-rupa.

The 1st thing inappropriate attention attends to inappropriately are the internal sankhara.

MN 19 describes how the Buddha-To-Be attended appropriately to the internal sankhara.

And as I remained thus heedful, ardent & resolute, thinking imbued with sensuality arose in me. I discerned that 'Thinking imbued with sensuality has arisen in me; and that leads to my own affliction or to the affliction of others or to the affliction of both. It obstructs discernment, promotes vexation & does not lead to Unbinding.'

As I noticed that it leads to my own affliction, it subsided. As I noticed that it leads to the affliction of others... to the affliction of both... it obstructs discernment, promotes vexation, & does not lead to Unbinding, it subsided. Whenever thinking imbued with sensuality had arisen, I simply abandoned it, dispelled it, wiped it out of existence.

Whatever a monk keeps pursuing with his thinking & pondering, that becomes the inclination of his awareness. If a monk keeps pursuing thinking imbued with sensuality, abandoning thinking imbued with renunciation, his mind is bent (namati) by that thinking imbued with sensuality. If a monk keeps pursuing thinking imbued with ill will, abandoning thinking imbued with non-ill will, his mind is bent by that thinking imbued with ill will. If a monk keeps pursuing thinking imbued with harmfulness, abandoning thinking imbued with harmlessness, his mind is bent by that thinking imbued with harmfulness.

MN 19

Note: the word "bent" above is "namati"; which, according to Buddhaghosa, is the verbal form or action of "nama". Buddhaghosa said: "why is it called nama; because it bends (namati); thus it is called nama". "Inclination" above is also related to "nama".

When the mind is bent inappropriately with inappropriate inclinations, this is ayoniso manasikāro (careless attention).

When the mind is not bent inappropriately, this is yoniso manasikāro (careful attention).

This is why knowing exactly what nama-rupa is is important. Nama-rupa is the 1st line of defense against ignorant sankharas.

At the first point, avijja, see lokutara-Dependening co-arising/disapearing, Upanisa Sutta, for easier understanding in relation of the cited sutta and the doubts.

Not hearing, reminding the good Dhamma, no Saddha/Sila: Samsara.

This, how ever, is a matter of Upanissaya, strong conditions and thete given causes: lack of proper birth and missing of Dukkha.

[Note: not given for trade, exchange, stacks, Buddh-ism, bounds to the world, but to be used for liberation]

MN 148 (my emphasis added) ...

Mind consciousness arises dependent on the mind and thoughts. The meeting of the three is contact. Contact is a condition for what is felt as pleasant, painful, or neutral. When you experience a pleasant feeling, if you don’t approve, welcome, and keep clinging to it, the underlying tendency to greed does not underlie that. When you experience a painful feeling, if you don’t sorrow or wail or lament, beating your breast and falling into confusion, the underlying tendency to repulsion does not underlie that. When you experience a neutral feeling, if you truly understand that feeling’s origin, ending, gratification, drawback, and escape, the underlying tendency to ignorance does not underlie that. Mendicants, after giving up the underlying tendency to greed for pleasant feeling, after dispelling the underlying tendency to repulsion towards painful feeling, after eradicating ignorance in the case of neutral feeling, after giving up ignorance and giving rise to knowledge, it’s totally possible to make an end of suffering in the present life.

... so maybe unwise attention happens at the "feeling" stage (and the converse is "guarding the senses").

You could probably say it's associated with other nidanas too, e.g. ignorance (which is arguably the "root"); and/or namarupa (per the definition you referenced here, i.e. that nama includes "Feeling, perception, intention, contact and attention").

Also MN 2 says that the "thicket of views" associated with self-views arises when attending inappropriately -- and MN 148 (quoted above) also says it's possible (but wrong) to identify with eye, eye-object, eye-consciousness, contact, feeling, craving, etc. -- so maybe that would be some inappropriate attention associated with all of these nidanas.

But because AN 10.6 says it results in "restraint of the sense faculties" I think that's talking about "guarding the senses" and therefore e.g. not delighting in feeling.

Maybe not "before" sense contact though -- before and after. I think the DO relationship is more complicated than strictly chronological e.g. "once around the clock, clockwise".