The question I'm focussing on here is: why Need can be used only one time in TAR (and in finding Green Man's place)?

The Wise Ones told Egwene, that wanting to use the same need for a second TAR-search would be like wanting to eat the same apple for second time (it wasn't exactly apple in the explanation, but never mind, the sense is the same). Such an answer means IMHO that thay at least intuitively understand some bit about how need-search works. Else they would say "it is just so in TAR" but wouldn't give explanations. I'm not saying that they understand enough, but they definitely feel, that using needs for search destroys something one had earlier. I.e. there is some resource in human, called the "Need" that allows search for dreamwalkers, and that ressource allows only one single search per unit of Need.

It's clear that here is nothing to do with the "real is what you believe to be real" paradigm, that is so often proposed to explain everything about TAR. Elayne and Nynaeve tried, but they couldn't do it, and only after that failed attempt Egwene told them it's impossible. And if it was just belief, the using of need would create a inner block against using it second time, but we see in the example of the Wise Ones the group in WoT that is most immune to any kind of psychological traps and blocks, so that makes the hypothesis that the belief works in the need, not so likely.

Wise Ones use Need for forcing seer's information, and that is close to their other well known function - to see spontaneously important things in the future for the Aiel. The last is very close to foretelling, and also is close to what AS know about the talent of Dreaming. Fortelling-like effects are apparently based on reading the Pattern itself. It is the most likely option also for Need.

What is "need"? The conditions for a thread (or group of threads) to fulfill some requirements the context (and the historical context in WoT is the Pattern) gives them for the thread to can exist further keeping it's tendention. "Need" is what a thread needs for to fulfil it's purpose in the situation. "Need" was never refered to be subjective, illusionary need, only "real" "true" need could work in search and in finding the Eye of the World. So "Need" is an aspect of the relations between a thread and the Pattern, it is a function of the mechanisms of the Pattern.

When a dreamwalker concentrates on need, she is concentrating on a Pattern mechanism. So a Pattern mechanism is what is actually making the search, and the dreamwalker only attaches herself to the process.

A Need is also a tension in the Pattern. Actually a Need-search finds something that will solve the tension, that will neutralize it. After the answer is known, the something to solve the tension already exists for the person and the tension is no more there. But if the answer is not clear for the person, or more difficult and risky paces are to be done for to reach the solution, the person will still feel a need, only the need cannot be used for second time. So the tension is not in person's will and conscience, but in the process of the dreamwalker moving to the needed thing itself.

Once a dreamwalker begins to use Need, the process is stepwise. The dreamwalker concentrates of the need and comes closer to the goal, she concentrates for second time and gets closer, and so on. Between steps of the process the dreamwalker can ever add some moments to the need's formula and so change the direction of approach. So Elayne and Nynaeve when seeking for solution against the drought, first find themselves in Tar Valon, but they add "not in Tar Valon" condition to what they seek for, and they are moved to Ebou Dar. They made lot of steps after that. But once they made a break in the search they became unable to any concretizations more. So most decisive for the Need-search is the beginning of the process.

From the other side, the Pattern's need to control the world requires It's own mechanisms to find what is needed in situations. And this mechanisms also work stepwise. So it comes time when the Pattern needs Dragon, and crowds of false Dragons appear, at the end the real Dragon is proclaimed and immediately all the false dragons lose their battles. Also the Pattern uses single-chance solutions: for example the Dragon has to face DO at Tarmon Gaidon at some moment of time, and if the Dragon is killed before that, the history would have to wait to the next Tarmon Gaidon after Ages. Also the Aiel sept chieftains in the beginning of Rhuidean had a single chance to decide to enter Rhuidean, and the septs of all those who hesitated were lost. Also a ta'veren is known to become what the ta'veren needs (but what a ta'veren needs depends not on what the ta'veren wants), i.e. ta'veren's life is some sort of non-conscious practical Need-search in the waked world. Interesting here is, that a living person is used by the Pattern for to provide finding of what is needed.

That leads me to the suggestion, that when the Pattern wants to find what is needed for a situation, It investigates the need as detectable in human threads, and then It makes virtual connection to the object needed to fix the purpose of the person the Pattern based it's search on. If this connection would be available by the normal flow of events, the Pattern just lets it happen, but if there are issues, the Pattern changes the normal tendentions of other threads - and we have a ta'veren.

Now my hypothesis is, that dreamwalkers in TAR turn on the process the Pattern itself use to investigate needs. The dreamwalker gives the tension she feels as a base, and the Pattern processes it. The dreamwalker must concentrate on the need for to show to the Pattern exactly that tension, cleared from other stuff. In TAR the Pattern has it's reflection from all the parallel worlds, so a mere manifestation of a need will fit into the context of Pattern's own work. If the Pattern finds a tension in it's context, it processes it. The dreamwalker uses that to be together with the process. The dreamwalker is as if assisting the Pattern in a childbirth of a solution (that the Pattern usually does without any midwife). Unlike the objects a dreamwalker imagines in TAR, the need is something that really has it's place in the Pattern, so unlike the imagination-based objects, the Pattern reacts.

Once the search is done, the Pattern has the solution for it, and there is no need for it to repeat it. The Pattern doesn't care about how many the dreamwalker understands, the Pattern does the search not for the dreamwalker but for itself. The dreamwalker is only the initiation of the process. For the Pattern the tension is as if resolved. At least it is resolved for TAR, where the timeless reflections of everything are stored, and where the results of all mirror worlds are present. I.e. in TAR the actual fulfillment is not necessarily addressed when there are issues with needs. So a Need-search doesn't work second time with the same need.

Another example in the books of using Need is the search for the Eye of the World. The Green Man senses the need of those who search for him, and according to that need his place appears earlier or later in different places in the Blight. The Green Man said also that his place doesn't move, so it is some different dimension of reality against the dimension of reality where the Blight with the Mountains of Dhoom exist. When the Green man is feeling the Need, he is linking his place to the location where the thread is. It must be the thread, what is used by the Green Man to find the seeker of the Eye, because the Green man shows no orientation in the geography of the Blight territory or something else in the environment, and also he don't recognize people he hasn't seen before, for example he is thinking Rand is an Aiel, despite of it was most likely exactly Rand whos thread provided the Need.

What can be the Need, he is feeling? It's definitely not any kind of need, because many men went to the Blight for different reason, some of them specifically for searching for the Eye, and everybody entering the Blight will be in very serious need soon, the Bligth will guarantee some need earlier or later, but only few find the Eye. So it's not any need, that works here. Only the "true" Need is sensed. When the Need is the Need of the World, that Moiraine's group had, the Green Man finds them earlier then ever. In all other cases the Eye was behind the passes of the mountains of Dhoom, but in that case it was before the passes. I.e. the feeling of the Need depends of how important is the Need for the Wheel, or at least for the prophecy because of that the Green Man is there. Because the Eye is created artificially by the AoLer AS, and Someshta is also creation of AS, it is to be human will that set the rules. But the only motive to create the Eye was the prophecy, therefore any human will responsible for creating the Eye and it's rules, is serving to the prophecy, and the prophecy is Wheel's will, so the last instantion determining the rules of the Green Man's place will be the Wheel. AoLer AS could determine what kind of Need should Someshta sense, but the only kind of Need there was sense for them to determine was the kind of Need specified by the prophecy, i.e. by the Wheel. So Green Man's place is analogue to the Wheel's mechanism to calculate needs, and in the Rand's case it is one of the Wheel's mechanisms to find the needed actually. Maybe with the most of others who found the Eye it was just the usage of similar kind of Need to the ultimate. But Rand in tEotW is case when the Wheel itself is working, and the Need seems to fit in the same way of functioning, Wheel is usually using.

The fact that usually one cannot find the Eye two times (Moiraine is the only exception, as Someshta said), while the Green Man himself have no motives to neglect the second need, means that it must be the Wheel's mechanism again, or at least some good equivalent of it, that determines the rules. The Need is sensed in somebody's thread, the connection to the Green Man's Place is done and for the force that is responsible for the Need-sensing there is no Need more, whatever happens with the corresponding person later: he is already connected and the Need is over. It's possible only in the Pattern's point of view, where there is a singular thread among other threads, whole one for differents moments of time, and the Need is applied to the whole thread, not to a particular moment of life.

Moiraine is coming second time to the Eye, actually using the Need of the three ta'verens. She is the one who is really responsible for the whole adventure though, she is the actual leader. But already in Baerlon there was viewing about the group of the three boys, Moiraine, Lan, Egwene becoming together into the same one thing. So it was that compound thing, that complex bundle of threads that had the Need. Moiraine was the leader, but actually that is similar to the role of the dreamwalker in the stepwise Need-search. Moiraine is assisting to the coming of the Need on the surface, well visible for the corresponding Wheel's mechanism. Moiraine was not the mother but the midwife of that Need. She had a ready Need near her, and she makes it to become more visible. The same make the dreamwalkers in making the Need more precise. But initiating the Need needs real need and it could be done only one time.