I blink at them first. Then look at there eyes. If they don't blink back I blink again but slower (keeping my eyes shut for 1 second). If they still don't blink back then I blink for maybe 2 seconds, and then I look to see if they blink back.
If they don't, then I consider them unapproachable.
I have found that deploying this method usually cats respond by coming to me, rather than me going to them. They rub their heads against my feet (one of the scent glands of cats is near their cheek. They use it to mark territory). Then usually their tail points up, and then I stroke them.
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We, the people on the Autistic Spectrum have a choice.
We can either try to "fit in" with the rest of society, or we can be so egocentric that we can't be bothered.
I choose the actor. I observe NT's. I listen to their socializing. I practice it, so in social situations I can just emulate/mimic what is expected.
It isn't natural for me, but it enables me to "fit in".
It is VERY tiring and draining, but at least we can appear like them even though it is an act. Like being on the stage.
They can't see it is emulation, and so we are accepted.