A proper understanding of the aircraft systems is simply put airmanship.
I teach in Airframes and Systems and that is what I tell my students.
Once airborne you have the weather, and you have the plane and the aerodynamic laws and yourself and a colleauge. Ofcourse, rules of the air must be followed. But when the plane breakes down and is degraded, the rules don't apply anymore. In that case, knowledge is your best friend. Knowing that it takes 20 seconds to shut down an engine with the fire handles may be worth a lot when the time comes.
And knowing which systems affect other systems. In my case on the little Saab, the fuel is heated by prop gearbox oil. If we get a fuel temp low warning, the pilot with no particular interest in systems design may dive into the the checklist for "fuel temp low". In the mean time the prop gear box might fail due to lack of oil (hence lack of heating to the fuel) and this could have been easily averted by looking at the prop oil indicators as an instinctive reaction to the initial fuel temp low warning.
This kind of reaction isn't in any book. It requires an interest in what we are actually doing and an interest in our surroundings.
Bel Arg, you are truly a wealth of knowledge! Thanks for all the good tips and keep them coming!
/LnS