I do that too auntblabby and was so proud of myself until I realised from this forum that I almost certainly have odd eye contact, and as you say it isn't fluent. For this reason, apart from the golden rule, I have given up trying to learn social skills for my own sake as
I can see there will always be leftover oddness. It may even be more disturbing if it only falls short by a tiny margin.
This becomes more difficult when someone says "just do this" and I know I can't pull it off but can't get them to understand that.
They haven't grasped themselves how very complex their behaviour is.
Although my husband hit the nail on the head when he said "when they tell you just be yourself, and don't like the results, they really meant, just be MYself"
I realise I have derailed my own thread, but that is conversations for you 
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"Aspie: 65/200
NT: 155/200
You are very likely neurotypical"
Changed score with attention to health. Still have AS traits and also some difficulties.