It does move. It prefers the shady areas and not bright light.
It was on the bottom of the same rock as yellow leather coral that suddenly died after I had it for 2 months. It had a cut in it's stem and it started to dissiolve in 1 week's time.
It doesn't look like a nudibranch to me when I compare it with photos on Wikipedia?
It does not have a tail or head.
I will try to take a better picture.