My read on the situation is that, when people say pencil jump, they are simply referring to jumping without holding crouch.

However, the name actually has it's origin in a peculiar pose of the soldiers model, where his legs are completely straight.
From my brief testing before writing this post, simply letting go of crouch will cause the solder to do a 'windmill' motion, where his legs look like they are walking.

Does anyone know how to consistently replicate the true pencil form?