For me, mostly visual stims

. Very hard to detect for someone on the outside, aside from the classic "side-eye", of course. I dis align my eyes so that I see double, then line up the double image in different ways. Make my vision blur and make the lights dance. Stare at intriguing patterns, trying to figure out all the ways they interlock. All sorts of things, and no one notices, at least I don't think they do
More obvious ones are usually reserved for when I'm very upset, excited, or concentrated. Rocking back and forth and side to side, head shaking, hand waving, arm swinging, head banging, biting, etc. Rarely ever in front of other people. When I'm anxious, or watching a gross scene in a movie, I lightly pat my head, or the air beside it.
Stimming can look like anything, or look like nothing.
I wish I could do the bit with your eyes. That sounds like wonderful fun.
I sing and hum to myself. I think no one can hear me, and then a stranger in the grocery store will comment on it.