Since it is an optional one ("just" guarding a Stray Bead) you can ignore him and still enjoy the entire story without missing out on anything, but the little completionist in me just HAS to beat him every time.
In the Switch version you can record and replay the clip, then solve the "puzzle" ingame as long as you don't let go of the brush button for the entire time (otherwise it's an automatic fail). The PSII version does not offer this workaround, and after a couple dozen tries I got so impatient that I grabbed an erasable marker and drew the lines between the dots on the TV screen. Still took me three more tries to actually beat him.
I don't doubt that there are some people who didn't have any problems with Blockhead at all, but I'm curious about possible other workarounds. So, how did you do it?