How Annie Proulx's Jack Twist and Ennis Del Mar reacted to each other in the parking lot at Aguirre's trailer is not known. They shook hands inside the trailer in her version. Forgive me if I am repeating myself in this dicussion, please.
We have to realize that the movie was not a produced by out of the closet male-gendered homosexuals nor was the screenplay adaptation written by openly gay men.
I actually don't call what was seen in the movie the same thing as when a woman flirts with a man or vice versa. I have had women flirt with me in public places lots of times.
But, in the way that Jake Gyllenhaal portrayed Jack Twist and his use of facial expressions and body language, implies that Jack had a below-the-belt, behind-the-pubic-bone, in-the-area-of-the-prostate physiological sexual attraction (PSA) feelings directed toward Ennis Del Mar. One has absolutely no control over when one experiences those PSAs sensations; they just happen without warning and they tell the one having them that the other person might be sexually compatible and possibly in one's comfort zone.
While the movie Jack at first seems to size up whom that guy leaning against the trailer wall is as soon as he gets out of his GMC pickup truck, the way he acts after that is not what I call flirting. Jack is acting according to what he feels down inside his body.
And being a man who feels that he understands same-gender PSAs and why they happen, I would say that the movie Ennis did not rebuff Jack by lowering the brim of his hat; he was doing his version of "I am attracted to you, too: but, I don't want to seem that obvious" act.
I know that Ennis did not understand how he experienced those PSAs directed toward Jack in his presence and he called them "that thing that grabs us in the wrong place at the wrong time and we're dead" queer feelings.
While women, no matter what their sexual orientation, can agree or disagree with me in what I consider to be fact or related to my POV, I don't feel that women don't understand openly gay men much better than heteroseuxal men and heterosexual women understand each other. Some women to have special insight to certain facets related to a gay man's makeup; but, they still have to rely on what a gay man tells them to know why they have such insight.
Oh, if you will notice I am also open about my gender in my forum profile. But, while human beings are generalized as either male or female when it comes to identifying by a 'sex (gender)," there is two other genders which are in existence with humans, Intersex (which used to be commonly called "hermaphrodite") for double-gendered persons and "asexual" as in having no gender known at all, but might assumed to be female because of the lack of external genitals.
To wrap this posting installment of my up here, I think that Ennis (no matter what version) was actually hesitant when it came to meeting new people and it was related to his lack of self-esteem and the hard life he had growing up. And because his father spiritually and psychologically abused him by taking him and his brother, K.E., to see the beaten to a pulp with a tire iron mutilated body of Earl, he was afraid of being an "Earl," too and possibly becoming a part of a same-sex ranching couple.