Nathaniel Branden provided the solution based on Rand's observation that the non-choice of non-thinking is a blank-out, an avoidance of choice, and it is not rational or conscious, but emotional, below the conceptual level.

It is a little trickier than that. There is a signal that the conscious mind receives, coming from the subconscious when the subconscious starts initiating a blank-out.  It is the cue that the conscious mind gets to CHOOSE to acknowledge and initiate focus or CHOOSE to ignore at the conscious level and let the blank-out proceed.  And that choice is one of the key events in increasing or decreasing self-esteem. The subconscious starts to initiate the blank-out as defensive routine.  And it is over time that self-esteem slowly increases or decreases, and at the same time there can be a pattern of choosing to go along with the blank-out or the choice to resist the tendency to 'look away'.  This is important because our psychological nature is such that we can't continue to not think except by choice.  If we choose the blanking-out then we will build in stronger and and often more complex defenses - usually levels of defenses - making future blanking-out easier.

The other complication that comes to mind is that this is an iterative process. A computer processes thousands or millions of tiny instructions per second and it is only by organizing these into functional routines where patterns of instruction processing provides a purposeful result.  We have 'routines' in our minds that process their input and generate output.  And many if not all of the routines send output to whatever part of the mind we might imagine is doing the choosing. That 'choosing routine' is receiving results from many sources - from our reasoning on a value, then from comparisons of that output with output from other values, emotional responses - those from defense mechanisms, those from imagined outcomes that are too optimistic, from those that are pessimistic. Sometimes it seems like one of those play-off charts where all the teams line up at the start of the season, and the winners of there first round of games go on to the next round. But its hundreds of times more messy and with the results of a couple of different rounds going through some kind of mixer then being fed back into a spot earlier in the chart. And it is not just iterative, but on-going - ubiquitous - never ending and just a way of describing our mental process. But we don't know much about it, certainly not down to the neurological level, and not even as a model of the mind at a gross level... because we are only aware of what is conscious and the rest is theory.

Hence, the call to be rational, is a call to stay more aware of how we are focusing, and to listen to those little signals that say we are blanking out. And to ask ourselves questions because that seems to be a way to keep emotional input from weighing in as much as if were cognition.  But this is about our psychology - and coersion in this context is a moral issue as well.
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...as Rand pointed out, coercion removes free will.

It doesn't remove the capacity to choose. It doesn't remove the existence of things to choose between. What it removes is freedom. You still have the ability to "will" but it not a "free will". Where there are actions that were one's right to take, but that under the gun one can't be taken as one would have if the will were free. The value-will connection has been short-circuited. The victim can still make choices, and there are still actions to choose between, but to take that act ones mind WOULD HAVE called for, an action that one has the moral right to take, is what is gone.  If you are about to eat some chocolate ice cream and someone puts a gun to your head and says, "Eat that ice cream" we would be worried because of the craziness, and we would be concerned about coersion as not being a good thing, but we can see that it doesn't short cut the value hierarchy in the sense that we are being ordered to take an action that lines up with our values in just the way we had already chosen.  But it would be very different if the person said, "Take your spoon and stab yourself hard in the eye, or I'll pull the trigger and kill you."  That would really put a disconnect between our values and our choices.

Conciousness and reason tells us about the universe outside of our skin. Reason lets us create/adopt a hierachy of values (even if we are irrational, we will find ourselves with some kind of hierachy - values can't be "held" in another way).

Life and the universe require that we act to gain values or die.  Choice is that inner part of the connection between values and living in this universe.  The external part of that connection is the action taken on behalf of the choicen value.  The gun at the head severs the connection between the values and actions. You still hold value A which calls for action B, but now, on the inside while you still have value A and want to take action B, but you can't or the result will be death which invalidates the entire process of a life that is the acting to gain and keep values as you choose.

In psychology when you have a severe conflict, it is usually between a defense that is hiding its motivation and a powerful value.  Say a priest holds the belief that to feel lust is a terrible moral failing, but when he sees a young woman in a short skirt... he lusts.  He builds defenses that are mostly forms of avoidance - blanking-out the arousal.  But over time pressures can build in the subconscious and given the power of the sexual drive, the conflict breaks through the defenses and his repressed feelings burst out.  His feeling at that moment: "I must not feel this lust under any conditon, but I do and I can't stop it."  He can resolve this because it is an interal conflict.  Another person may hold conflicting beliefs - like a mixed economy, a person may be part altruistic in their thinking and part egoistic.  This too is an internal conflict and can be resolved.  But a gun at the head is not internal and the source of the conflict isn't available in a way that allows chosing to resolve the problem.