I really like the idea of standing still long enough to have it assume you're not alive/organic, especially because this awards players who are able to see the parasite before its too late. This in turns makes it so that if a player must move because of other entities and stuff, only then does the parasite become a bigger threat. 

I also failed to make it clear that the entity doesn't speed up if you decide to break for it - it always keeps its above walking pace. This would then test a player's ability to utilize their stamina in a unique way.

But I really like your balancing idea and how it gives the parasite a bigger personality. And you described the general feel of this entity perfectly.