I am, by no means, an expert in Eastern Monarchies or Mesoamerican ones, but I think you have to be careful to negotiate the 'divine right' that Western and Byzantine kings employed, versus those of Egyptian pharaohs, versus those of the Far East. Because most of us in the West have at least a marginal understanding of how the divine right schema was wielded it feels on the surface similar, but in many ways it was not. If anything, the true similarity comes from justification and/or entrenchment of one's ruling position, rather than a similar actual claim. For example, while the Mandate of Heaven found in Chinese dynasties seems very similar on the surface to the 'divine right' of western Monarchs, the differences are subtle but important. Indeed, I would argue that the idea of the Mandate was actually less a justification for rule as much as a justification for overthrowing said rule and garnering the new dynasty legitimacy for disposing of the old. The 'divine right' of western monarchs is pretty different from this, even if it might have similar origins. I think most historians would probably agree that the western idealization of the divine right flows from the Eastern Roman Empire's influences, with the success of the Emperor's reign being largely attributable to their effectively carrying out God's will, with their failures being held up as doing the opposite. This was often used (as in China) as a justification for the frequent usurping of that office. This sort of lays the seeds for the divine right that future Western rulers would use, however the justification is a bit different. In the West, what we see is a process of amalgamation and (at least attempts at) centralization. Charlemange's Empire is a good example of this. However, his Empire was short lived. It wouldn't be until the 15th and 16th centuries that greater amalgamation and centralization would take place in Western Europe, and here, these monarchs needed a justification for both the subsuming of smaller states into their own, as well as the growing control and authority they had over their own states. There was also the matter of dealing with the Church; the divine right became particularly in vogue during the years directly after the reformation, and was often used as either a justification for the reorganization of the temporal religious structures in a state, or for the defense of the orthodox structures that existed.

At any rate, both of these are very different that some of the older examples, even if they are bit connected, tangentially at least. I think that there's a very good argument to be made that the original Byzantine notion of divine right is a natural development of the Imperial cults and claims to diefied status as well as the ceremony those entailed during the first three centuries of the first millennium. In turn, those aspects were largely influenced by the eastern cults and religious ways found in Egypt and Mesopotamia. Mesopotamia is particularly interesting, because there, the role of secular and religious leadership was once shared between two people, and eventually amalgamated into a single position. Why is that? Why is all of this so similar? Why would the Roman emperors import eastern cult practices into the West?

The answer, going back to the beginning, is justification and defense of power. Now, it's certainly possible (even likely) that some of the leaders of these states genuinely believed in their divine status. However, I suspect that most probably realized that amalgamating the temporal and spiritual authority into a single person/office was the most effective way of ensuring authority and compliance, and given that religious institutions have been some of the strongest methods of governance and control since the dawn of recorded history, it should come as no shock that rulers would attempt to insert themselves into them to benefit.

I'll leave this supposed quote from the Emperor Vespasian from his death bed: "Dear me, I must be becoming a god!" Vespasian was known for his straightforward ways, and we can probably assume he was being sarcastic here (or at least, the person who made it up was attempting to convey that point). This was in the early Imperial period still, so the really regimented and divine nature of the 'Emperor' position (or at least claims to divinity) are quite a ways off.

I don't have the book now, but you might take a look at Kingship: The Politics of Enchantment by Francis Oakley.