I have now read all of Robert Shea's Shike, which is really one work of fiction but originally was published as two novels, Time of the Dragons and Last of the Ninja. I read the first volume a few weeks ago and I've now completed the second volume.
Shike was first published in 1981, and it launched Shea's career, after he was laid off by Playboy magazine, as a successful historical novelist. Shike is set in thirteenth century medieval Japan, during the era of Kublai Khan (1215-1294) and the Mongol invasions of Japan.
While Shea's All Things Are Lights remains a great favorite of mine, you could also make a case that Shike is his best work. It's very well plotted, very vivid with nonstop action and romance. The action roams across much of China and Mongolia as well as Japan. There's a lot about Zen Buddhism, a big interest of Shea's, about Mongol and Japanese military weapons and tactics, and about Shea's mystical views. The word "Illuminati" is not mentioned, but the main hero belongs to a secret society, and it's explained that the group has ties to other groups, such as the Knights Templar. The analysis at the Wikipedia entry seems accurate to me.
All Things Are Lights and Shike take place at about the same time in different parts of the world; Shea's other medieval historical work of fiction, The Saracen, also is set in about the same period of history, with events a little later than the events of All Things Are Lights.