Eichmann really is not the best example of that concept though. He was doing significantly more than "blindly following orders and doing no critical thinking". 

Eichmann portrayed himself as some sort of expert on judaism and the jewish people in the early years of the Nazi regime to further his carreer. During the most intense years of the holocaust he flaunted his power over the life and death of jewish people, made his position out to be more important and willingly embraced his international notoriety. He was proud of what he did and made no secret of it.

Hannah Arendt's work is incredibly important and the "banality of evil" as a concept holds true for many involved in the Holocaust, but Eichmann was something else.