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Let me say how much I appreciate your thoughfulness on this critical issue for there is much more than just the subject of morality at stake. If there is, in fact, a divine presence from which morality comes into being, then all mankind needs to understand this presence, what is demanded from it, and the cost of rebellion against it. If the cost is merely returning to the dust from which we came, then morality may not be a big deal. But if the cost has eternal consequences, I want to be absolutely certain what I believe and why.

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Am I right to assume that moral/natural law necessitates a divine presense?

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I believe yes.

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If so, how does one make the connection to understanding the nature of that presense?

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As a Christian, I believe that God has solved that problem for us. More than 600 years prior to the event, the prophet Isaiah foretold of the coming of Immanuel which means "God with Us". Specific aspects of the life of Immanuel were also predicted in great detail by Isaiah. Many other prophecies foretold the same but I point to Isaiah because the copies of this writing found in the Dead Sea Scrolls preceded Christ's birth by several hundred years, i.e. they weren't made up after the fact. Jesus Christ is, in fact, God in human flesh who came so that we could see and know who God was and what He was like.

Therefore, you can easily begin to make this connection by reading what the Bible has to say about Jesus. While any of the four gospels would suffice, a great place would be the Gospel of John which was written by one of Jesus' closest disciples for the purpose of explaining that this man was indeed God in human flesh.
For someone who is a self-described "rationalist" (I have been so described), I would recommend reading The Case for Christ by Lee Strobel.