Like most modern negotiation trainers, I teach not to focus on positions but on interests. Awhile ago I gave a seminar, and one of the participants told me he doesn't want ever to disclose his interests, because then his negotiation partners will know what to withhold to put pressure on him.
Let's leave aside the notion that there has been no trust at all established, and that he may be contributing subtly to that distrust, maybe by non-verbal communication. What can he do? He has an important or even key interest, but is afraid of saying so.
Here's an idea to get around his problem. Instead of laying out for the other side what his interests are, my participant could just come to the first meeting with a list of issues or talking points—an agenda of things he thinks the eventual agreement ought to cover. He need not unduly emphasize the one that is key for him until and unless the other party is also forthcoming.
Negotiation 101: It is important to avoid positions, instead focusing on your interests, if you prefer by presenting a set of talking points or issues, not all key to your happiness.