When an idea nudges at my writing brain, I tend to let it puddle around a bit until it takes a form that I see as logical, workable, and in the tone that suits my style.

Actually, the writing of a nonfiction book takes the author through stages akin to the four stages of creativity, as first determined by brain researchers in the 1920s.
Preparation is all that you already know about a subject or deliberately research for application to it.  It includes getting the idea and determining where additional resources can be found.
Incubation is that period when you absorb the preparation. It's the "mulling over" stage.
Illumination is when you come to your own conclusions, attitudes, or philosophies about the subject. Some writers call it 'finding your own voice about the material.'
Verification occurs when you apply to the exposition of your subject the particulars that are pertinent to the specific purpose and eliminate those conjectures or issues that are tangential. Here's where the real editing, revising, and polishing of the book take place. 

Right-brain activity brings out the creative side. 
Left-brain activity pulls on the editing side.