I actually read something with a similar villain. He was doing though because he thought the government wasn’t strong enough to maintain national integrity.
The best and time honored way is to find the middle man/men. (generals and other ranking officials) Once you know who he uses, show how he places them for their skills. From there one can look for the common denominator that is the big boss or the trail to him. As for how to reveal it, my suggestion is to have the main character think they have him figured out and get surprised when he moves to phase two.
The Devil saw me with my head down and got excited. Then I said Amen