When you see someone's life support switched off do you think the shaking of the body is the soul trying to make the body work?

Heh. You know these are the sorts of questions I like. They should be asked more. I like you.

Never heard of that in a life support option before but otherwise where it happens called variously the death rattle, the big exhale, the last few hiccups.

I'm gonna guess at it. Probably the brain's electric frequency (the soul, if you will) shifting phase resonance with this current dimension's harmonic to another or something like that.

I never remember seeing any such reaction.

Who knows. I don't believe in souls, so I would imagine it's normal physiologicl responses.