In both Rāmāyaṇa and Mahābhārata, we see Indra taking a human form during what appears to be emergency situations.
When Indra wants to rob Gautama off of his ascetic power he suddenly decides to take a human form which is an exact replica of Gautama.
Similarly, to try and disrupt Viśvāmitra's penance to become a brahmarṣi, Indra suddenly appears before him as a brāhmaṇa and begs/steals his only meal in a long time.
In Mahābhārata, Indra again presents himself as a brāhmaṇa (out of thin air) to steal Karṇa's armour.
First off, are these on-demand assumptions of human form considered incarnations/avatars?
Secondly, how do gods decide when to follow the due process i.e., enter a mother's womb and take birth in a certain family. And just drive the events that just lead up to the actual purpose of their incarnation – versus – just taking the right human form at the right moment?
For example, in Gautama's case, why didn't Indra just take birth as Gautama's twin brother?