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I'm currently trying to map out my intriguing puzzle box, in the hopes that someone will eventually be able to figure out what the pattern of clicks, beeps, buzzes, and numbers represents.

187 iterations fully mapped, 209 known iterations

t-	turn the
p-	push the
-t-	top face
-b-	bottom face
-f-	front face
-x-	rear face
-l-	left face
-r-	right face
-c	clockwise
-cc	counterclockwise

Also, I got sick of having to input 80+ commands every time and decided to automate the process. KoLmafia doesn't support the puzzle box at all, and I couldn't find a Greasemonkey script anywhere, so I cobbled together my own pathetic Greasemonkey script that automatically clicks through a hardcoded series of buttons.

It's not really fit for public use (you'd have to manually rewrite the list of buttons to click, and you have to disable it after it's finished or it starts clicking again), but I'm publishing the source code anyway in the hope that if someone decides to make a good puzzle box script it'll save them some time or something.