Earlier quoted context omitted.
My family calls that game "pink mink"!
As far as I know the most common name is "hink pink", if anyone wants to look this up (or sometimes "hinky pinky"). Here's a 1981 book, https://archive.org/details/hinkpinkbookorwh00burn/ and here's a short description from the 50s, https://archive.org/details/realbookofgames0000unse/page/134... Searching further, apparently Hink Pink was the name of an 18th century pirate ship; I'm not sure if there's a relation to…
It's possible I found this decades ago and the origin of how I learned this game was lost to time :)