It might be different for each stutterer, but with me, some people tend to look away and loose eye contact when I start stuttering, I guess (subconsciously?) probably out of respect and not wanting to make my blocks worse by “staring“. Consequently I have been avoiding eye contact too, which made things only worse for me. The issue with this is, that eye contact is an important part of communication, it conveys so much meaning that gets lost without it. Also having somebody constantly looking away while you speak feels awkward. Since I noticed this, I focus on keeping normal levels of eyecontact, it greatly improves how good I feel in a conversation. I personally don’t mind if somebody stares at my lips, ist still better than looking away when I’m speaking. But having „normal“ eye contanct just feells so much better. If you don’t like keeping eye contact, it’s okay. I think the awkward part is when somebody suddenly acts differently, quickly looks elsewhere when you sttutter. So yeah, u/Extension_Salt_6995 summed it up great: Just be like you would be with a guy with normal communication.