LT asked, "So do you have any pets?" He said, "We have a few" but didn't specify."

I don't see his answer as "vague" at all. "Do you have any pets" is a yes or no question. He answered with more than a "yes," with "a few". LT could have simply asked, "what kinds of pets do you have?" I don't see this as difficult nor does it have to be the tortured ones that you presented. It's a lot easier to ask a question than be annoyed you don't get the answers you want.

In interviewing, this is called a follow up question. I believe this is very much how "neurotypical", or people with good communication skills, talk to each other. IMO it is better to ask a follow up question if you want to know something, as opposed to assuming a person doesn't want to answer. It would be great if everyone told us everything we wanted to know about whatever we want to know, but IME the truth is that we often have to ask. Sometimes people seem to be reluctant, but it is not often because of the asker, but because of the person answering. Sometimes they have to figure out how open they want to be, or how they feel about answering the question, or probably a few other things too.

At least in my way of doing things, I get the answers to the questions I want. If someone tells me no, I respect that and don't keep asking the same question. But my T has never refused to disclose anything I've asked, some of which has been personal with follow up questions, and a lot he discloses on his own. I know a lot about him and much of that is a result of my positive communication skills. But this is consistent with my experience in the world-- I like asking questions and my friends and loved ones like having me ask them. There's a big difference between learning about someone and being intrusive; and general interest in another person versus nosiness. I think people, including T's, can tell the difference. I see little reason for a T to refuse to disclose something where the client has a genuine interest in it and when they ask specifically in a straightforward way. My point is that communication requires effort on the part of the asker.