Is it the psychic will which wants the being to be identified with the Divine?

Yes, surely. It is the will of the psychic. It is also the very reason of its existence. It is for that it is there. For example, in the mind certain activities (and even at times in the physical and vital) ...awaken to the influence of the psychic without even knowing it. That is why those parts adhere to it and begin to aspire also for the divine knowledge, the divine union, the relation with the Divine.
                                                    
What is the work of the psychic being?

What is the work of the psychic being? You want it to have some work? What do you want to say exactly? What is its function? Ah! very well. One could put it this way, that it is like an electric wire that connects the generator with the lamp. Now, if someone has understood, let him explain what I said!

What is the generator and what the lamp? (Laughter)

Ah, there are! So, what is the generator and what the lamp? That is exactly it. What is the generator and what the lamp ? Or rather, who is the generator and who is the lamp?

The generator is the Divine and the lamp is the body.

It is the body, it is the visible being.
  So, that is its function. This means that if there were no psychic in Matter, it would not be able to have any direct contact with the Divine. And it is happily due to this psychic presence in Matter that the contact between Matter and the Divine can be direct and all human beings can be told, "You carry the Divine within you, and you have only to enter within yourself and you will find Him. " It is. something very particular to the human being or rather to the inhabitants of the earth. In the human being the psychic becomes more conscious, more formed, more conscious and more independent also. It is individualised in human beings. But it is a speciality of the earth. It is a direct infusion, special and redeeming, in the most inconscient and obscure Matter, so that it might once again awake through stages to the divine Consciousness, the divine Presence and finally to the Divine Himself. It is the presence of the psychic which makes man an exceptional being- I don't like to tell him this very much, because already he thinks too much of himself; he has such a high opinion of himself that it is not necessary to encourage him! But still, this is a fact -so much so that there are beings of other domains of the universe, those called by some people demigods and even gods, beings, for instance, of what Sri Aurobindo calls the Overmind, who are very eager to take a physical body on earth to have the experience of the psychic, for they don't have it. These beings certainly have many qualities that men don't, but they lack this divine presence which is altogether exceptional and exists only on the earth and nowhere else. All these inhabitants of the higher worlds, the Higher Mind, Overmind and other regions have no psychic being. Of course, the beings of the vital worlds don't have it either. But these latter don't regret it, they don't want it. There are only those very rare ones, quite exceptional, who want to be converted, and for this they act without delay, they immediately take a physical body. The others don't want it; it is something which binds them and constrains them to a rule they do not want.
   But it is a fact, so I am obliged to state that this is how it is, that it is an exceptional quality of the human being to carry within himself the psychic and, truly speaking, he does not take full advantage from it. He does not seem to consider this quality as soqlething very, very desirable, from the way he treats this presence -exactly that! He prefers to it the ideas of his mind, prefers the desires of his vital being and the habits of his physical.

The Mother