Count like rhythmic tapping.

Same way you can tap your finger four times without counting, and you can do four taps four times without counting those.

Maybe more a musical skill.

I tried this right now and noticed that I count tap for the first time. But the most important thing is that all of them are different and form a repeatable pattern. So brain just remembers the sensation of the fourth tap and I can tap in fourths subconsciously for a while.

The other way to deal with this exercise is just tapping for the odd count in one place and for the even in another. So you know when the fourth tap is because you subconsciously know it was long enough time after the second one and it is in the right place on the table.

This is called subitizing (or subitization). https://en.wikipedia.org/wiki/Subitizing

no, i count to four or ten and reset

so you are thinking numbers then?

you don't think "one" every time you do something once. just like that you can train to not think "one-two" and not to think "one-two three-four" and so on. gets harder the larger the number, but it's a matter of practice.

Like bars in music? Like I can put on the metronome to, say, tic-toc-toc-toc (different sound on 1 vs 2/3/4) and will intuitively know when I've hit 2, 4, 8, 16, 32 bars. I just feel it. I might be able to use this method for counting, just hearing clicks, and count to 16 bars or something, while doing whatever else, even though I am like Feynman in not being able to talk out loud while counting.

Yeah, I guess? I’m not a very musical person :)