Consider your question in terms of simple mechanics, to suggest 'idle thought' provokes the idea that (like an engine) one is within a neutral range but may step into gear and move forward with the intent to manifest such thoughts into actions etc. Instead of something that has 5 gears, a neutral point and a reverse shift, imagine something that can be infinitely geared to all directions and still be pivoted upon the neutral point, and instead of asking "where is neutral or where does it go?" acknowledge what a neutral point has to offer instead of attempting to measure a space for it, because technically measurement is taken upon entering the first gear in any direction and will lead you somewhere, however neutral is so 'specifically because it has no direction and can be all directions if you so will it, thus what you are asking is as the spiritual cohan (probably spelled wrong). The question has moved your thoughts of neutrality into first gear hence the question is no longer relevant within a neutral range because it moves towards idealization and onto a manifest concept by further measurements. Forgive my wording but does this make a form of sense?
In light, in love, with gratitude and acceptance, we give thanks to all that is, the universe, our home, our joy
-To be 'One' requires 'Two' choices, to be free is to see 'three' ways beyond the horizon-
-Words are but symbolic platforms that hold meanings, meaning has a way of building mortal towers that fall upon immortal virtues-