Have you ever noticed that in near darkness, you can see things better if you look at them in your peripheral vision?
I have that same sort of experience with my work. Sometimes when I am looking directly at the page and trying hard to come up with sermons or lessons or materials of some sort, I can't seem to get anywhere.
Then, when I am occupied with some unrelated task like driving, the ideas about the sermons, etc. begin to flow freely. Of course, I usually cannot stop right where I am and take down the ideas - (I'm busy driving!) Even if I try to write it down or record it, the flow of thought becomes restricted again.
I've learned that I am better off to just let the ideas flow rather than to try to capture them right away. Instead I play with them for a while. I let them flow in images as much as in words, and try not to spoil the moment by getting too specific. Then, later I can remember the basic shape of the ideas and get them down on paper when I am free to concentrate.
So, what do I do in the study? I read the text I am studying. I jot down notes about it. I read cross references. I check time-lines or charts or whatever I have that might be suggested by the text. Then I dream about it a little. I juggle. I sort through piles on my desk. I read an unrelated book. I play my flute. Then I write a bit more and put it away to turn my attention to some other task.
That's the way it works for me.