A super neat and original idea, and the music feels fitting if a bit irritating after a long time. I love that you implemented custom levels, and that you included a cheat mode (though I got an "index out of bounds error" when cheating).
The game does get tedious after a bit, so I feel like this would be best as part of a broader puzzle game, maybe an Escape the Room type game.
One UI suggestion: Place a dot on the screen where the player clicks the first time, so they know the game has registered that click.