My thanks to everyone who has replied and made suggestions. The difficulty however remains. DO is presented in a cause/effect sequence. “If this, then that.”
From the Sense bases to death, this is clearly the logic of the list.
But in the first four, we don’t have a sequence, and some of the content of the first four seem repeated in what follows.
It doesn’t seem as though we can attribute this to a faulty transmission of the text: the same list is given many times in the canon.
It doesn’t seem as though there was a great mystery involved, as there is with the Christian Trinity. Buddhism prides itself on going right to the point and not getting involved in elaborate metaphysics. Where there is a subtlety, the Buddha either explains it in great detail or tells us not to bother with it.
I am led to conclude that something was there for the original listeners that was so obvious that it didn’t seem necessary to explain.
I would suggest, not as the real answer, but as a mere hypothesis of what the real answer might look like: punctuation.
Ignorance, Constructing Activities. Consciousness, Mental-Physical Being, the Senses, Contact, Craving, Clinging. Becoming, Birth, Death.
A little less concisely:
Ignorance and Constructing Activities. (The basic human condition, we choose and do without really understanding).
(Our life is made up of) Consciousness, (which is the engagement of) Mental (with) Physical Being, (which entails) the Senses, Contact, Craving, (and finally) Clinging.
(The bad beginning, decisions and actions made in Ignorance, plays out in the whole greedy business of physical and mental life. The momentum of this keeps us in the cycles of Becoming, (which entail) Birth (and), Death (over and over again.)
Just a hypothesis.