That's a funny and impressive sense of self awareness.
If I may, I wouldn't think of the recruiter as an authority figure (they have none...) Rather they are your partner. Their best case scenario is that you are a good candidate for their job and they get to fill it. Which is also your best case scenario!
So it's more about how do you get there together collaboratively - at least that's how I frame it in my mind. So when they ask for something I don't want to share I respond more from the frame that it's not the piece of info that would help right now but here's how we should play it.
If I may, I wouldn't think of the recruiter as an authority figure (they have none...) Rather they are your partner. Their best case scenario is that you are a good candidate for their job and they get to fill it. Which is also your best case scenario!
So it's more about how do you get there together collaboratively - at least that's how I frame it in my mind. So when they ask for something I don't want to share I respond more from the frame that it's not the piece of info that would help right now but here's how we should play it.
But your script is definitely a good start!