It's not explicit, but the "one big thing" the hedgehogs know effectively reduces to a triad of, "there is no truth only power," "trust and defend the system because you are it now, and it takes care of the people who support it" and, "protect insiders or be an ousider."
The strategies for foxes and hedgehogs are different. If you are a fox and know this about hedgehogs, you can lever them against variations of these axioms. If you are a hedgehog, you can usually succeed by betting foxes don't get traction no matter how spectacular their knowledge and displays.
The idea is if you practice these things, you're going to be lucky and stuff is going to work out. If you don't, you're the sucker at the table and you'll be preoccupied by conspiracy theories.
If you know this, some Bayeseanism, and some simple actuarial models, with practice you can play at a pretty high level. There are other great books on this like Pfeffer's "Power" (https://www.amazon.com/Power-Some-People-Have-Others/dp/0061...) that describe the game once you have those rules.
May the odds be ever in your favor!
Leadership is not an activity or an action you can mimic, it it is an effect. Most books are the stories people tell afterwards about how virtuous they were and they call that leadership. Jeffery Pfeffer says this specifically as well.
Pfeffers books on management provide the insight into the dynamics leadership emerges from. His triad of, "performance, credentials, and relationships," that describe power in a situation also describe the necessary factors we look back on as leadership.
I like Jocko Willnick's whole attitude about ownership, respect, delegation, and working with people to leverage their skills to achieve outcomes. He says the hierarchy in the military isn't as much of a factor as how you relate to your team and the world, but I suspect Pfeffer would disagree in that its hierarchy and training culture provides the credential piece in his triad, where in business, that's more dynamic.
There are lots of good books about leadership, but reading them without having read Pfeffer's "Power.." is exploring the territory without the map, imo.