I remember playing a slightly Go-like game in primary school, using pen and paper. Both players have a pen of their own color (typically pencil and ballpoint) and take turns drawing dots at intersections of a rectangular grid. We called it Pistepeli ("point game" in Finnish) but Google doesn't find anything relevant with that name.
The objective is to surround some of the other player's dots, gaining a point for each one. This is done by completely encircling them, drawing a winding line connecting your own adjacent dots (along the 8 compass directions), only when you have managed to place all the required dots so the line will loop back to its starting point. You may not use your own dots that the opponent has already encircled, but you may re-use your own lines to draw an encircled area next to an existing one.
You may enclose as many areas as you can during your turn, after placing a dot. The game continues until time runs out or there's a dot at every intersection on the paper, and then the game is scored by counting opponent dots each player has surrounded.
I can't remember if there was a rule that drawn dots must be next to an existing dot or specifically also of the opposite color, and how edges of the playing area were treated. Possibly it was forbidden to surround your own dots and/or empty intersections.