Very good discussion about eye contact. It's interesting, too, not just from the characters' viewpoints but because of what it says about the actors' and director's choices.
One thing that strikes me is that in the scenes where Ennis and Jack are actually discussing their relationship rather than just acting on their affection for one another, there is always an eye contact issue. In the "one shot thing" conversation, Ang shoots Heath over his shoulder so that only the right side of his face is seen as he talks to Jack. When they say goodbye in Signal, Ennis shoots glances at Jack as he squints into the light, but he never really sustains the eye contact. In the motel, Ang chooses to position them so that they never have eye contact. In the camping scene after the reunion, too, Ennis rarely looks at Jack as he explains why they can't live together. After the divorce, though Ennis does look at Jack piercingly at times, he often looks down or away. In the scene at the lake, Ennis avoids eye contact pretty much until he decides to confront Jack about Mexico. After that, the eye contact is finally full on for both of them until Ennis turns away to cry. As for Jack, in all of the aforementioned scenes, he is usually seen looking directly at Ennis for the most part. Even though there are a few times Jack looks away as he speaks to Ennis, in general he is the more direct of the two, always seeking to make contact, or at least to gauge Ennis's feeling.
This may be a topic for another thread, but for the most part Ennis owns screen left and Jack owns screen right when they are shot together. Exceptions are the handshake outside the trailer, the campfire scenes before Ennis switches jobs with Jack, the second tent scene, the introduction of Jack to Alma, and the beginning of the lake scene. Even in their individual scenes with other characters, Ennis is often on the left and Jack on the right. Could Ang have had a reason for this? Left and right can symbolize passive/active, malign/benign, emotional/practical, hidden/open. Perhaps something like that was at work here.