This is probably a stupid question but I need to understand this instinctive printing. Do those who print by instincts (and not do a test strip) always develop the paper at the same time or does the time in developer very according to what they see as it develops?
Just to be clear, in case I'm one of those you are referencing, I don't print by instinct at all. Intuition and instinct are not the same thing. Also, most people think that intuition is something like extrasensory perception. It isn't. You could call it "experience", I suppose, but that's not quite right. Experience is what trains the intuition. Lee is right, though, if we can agree on terms. Making thousands of prints helps a lot; especially if you think about it while you are making them!
Also, to answer the question you ask, assuming it is addressed to a group of which I'm a part, I do make test strips but not graduated test strips, one pop and develop, and I NEVER vary the development time. ONE VARIABLE! Everything else is held constant. If you start working with a bunch of variables, you can't ever learn because you really can't know what is producing the result you are getting. When students tell me that they are "messing around" (common!) we have a very pointed discussion.
Another helpful practice is to take a small piece of paper, cut it in half, put one half of it under something in the darkroom and take the other half out in the light for a few seconds. Process both at the same development time/agitation that you give your prints. Hold them in the tray you use to evaluate your test strips for comparison. Print for the white, by adjusting time or aperture, and when you get a white that comes close (it won't match exactly, at least if you care about detail, but it should generally be as close as possible without losing detail), then compare the black. As I mentioned above, if you can't find a black that matches the black patch, or if areas go black that should have detail, adjust the contrast accordingly.
Another tip: Always use the same light for making decisions about prints. If you don't, you are adding yet another variable. I used the same light for about thirty years, and since I'm building a darkroom now, the same light is going in it.