I guess the key part is that you're finding him draining already. I think we probably all have our own lines on how much encouragement to book that we give for free. I am kind to nervous clients but do stop giving them chances eventually as they do easily cross the line into timewaster territory.
In the room, they're some of my favourites, as they're generally slightly overwhelmed so easy to handle, and grateful for whatever they get, which is gratifying.
But sometimes all you can do is tell them you're ready to book when they are, and leave it to them to make the decision, and some never will.