I believe some of these insights may work outside of academia, but because I spent my life in academic administration (when I wasn't a professor) I'm not sure how many of them will transfer.
My mentor, and the man I most respect, was Jim G. Carleton, who taught my citizenship class freshman year and helped shape my life. He eventually became Vice Chancellor of Syracuse University and prospered under Chancellor John Corbally. He constantly fell on his sword so Corbally could make crucial changes to Syracuse (a place I love). When he left to become president of the University of Illinois, the people who had been resisting change took it out on my friend, Jim Carleton. He went back to the faculty. Later however, Corbally helped make Carleton VP of Northwestern (a step up in anybody's book).
Because I'd grown up without a father, I looked for individuals to model myself after, and Carleton was the guy I chose.
A wonderful man named Jack Brownell hired me to run a division at a Cal State school. He was in an acting position, and they brought in a president who I found really likable. The only flaw in my attempt to model myself after Carleton was that this man (The President) had left home at 12 and had accomplished everything on his own. He was an impressive guy but someone who could never conceive that someone would fall on their sword for him. I soon found myself being called into meetings with angry faculty at which the president would tell me how I screwed up. I certainly could've played this better, but I believed that you had to do what was best. The fact I wasn't being supported only angered me instead of warning me. Finally, I went back to my faculty position and lowered my visibility.
I don't know how many presidents there are like Corbally. I've met some, but I think you need to have his vision, and understand what you owe those who put themselves on the line for you, to be a great university president.
Unfortunately, the president I worked for in that last assignment, was forced to resign. That was not inevitable, and he had so many attractive qualities, it truly saddened me.