A cat of three years residence, the mother was frustrated that only her son was tolerated by the skittish animal. No lap, no pets, just distance. They went out of town for a few days so I was to cat-sit. First night, I sent a picture of the cat in bed with me, not quite touching.
I had done some experiments and the cat just did not like eye contact at all. Additionally, she prefers to be at fingertip distance, if one stretches. I sat in the bed, next to and facing the wall. Ten minutes of headboard staring in, the cat is parked about six inches behind me.
Full Raiders of the Lost Ark mode. After my suggestions, the cat was less distant. Now, when I visit, I put my jacket on the couch about three feet off. Poof, a cat appears on my jacket. I do not acknowledge. Sometimes my hand dangles near the floor and I get a brush-by. That is what she is comfortable with. You have to take them as they come.
All cats are neurotic; each cat is neurotic in its own peculiar way.