This is quite an interesting idea and it does make me more intrigued at the thought of a puppet type job. I do have a couple of questions tho.
What's the weapon? I'm not sure it could be the statue cus that has to be animated. It would make more sense for that to be a pet (and then you'd hopefully get statue glamours like we do now with egis).
And am I correct in understanding that your skills are your statues skills? If so, then you'd only have the 1 summon and the job would play differently than if your puppet had it's own skills because then you could have different ones for different situations.
Also, I don't think the job would be able to switch roles like that. Based on what happened with Red Mage, it would have 1 role with some utility.

If you have time, you'll have to flesh this out a bit more ^^ I'd like to see where it goes =)