short-term thinking
It appears that, sometime in the past, someone either taught Giovanni to be a shoulder-and-neck-sitter or declined to discourage the behavior. That's really cute with a 2-pound kitten. Ahem: they do not stay two-pound kittens forever. This is a terrible picture (Giovanni loves to investigate the camera instead of sitting still if he detects it), but to get an idea of scale:

And here are a couple pictures of Orlando:


Orlando did not go into hiding again after the vet visit, and yesterday afternoon he spent an hour or so in my lap in the living room (yay). Giovanni likes my office, particularly the computer desk, but is reluctant to explore the house much -- coming into the room next door while I was watching TV last night was a big stretch, and he's made some brief late-night forays into the bedroom. So far as I know he has not yet been downstairs under his own power. How do I nudge him along in that? I don't want a litterbox in my office forever.
For all the suitable places in the house, particularly for Orlando, I'm surprised that they both tend to sleep under the same chair in my office, concurrently.
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1. Take cat to clean litterbox
2. Put cat in litterbox.
3. Gently grasp cat forearms and make little digging/scraping motions in the litter, as though the cat were covering up waste. Four or five should do.
4. Let the cat go.
5. Walk away.
6. Repeat if the cat does not get the idea.
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I think I need him to be comfortable in the rest of the house first, and from there the boxes in the basement should follow. Orlando figured that out just fine. But I'm not sure how to get him to be comfortable in the rest of the house; possibly the answer is "wait another couple weeks".
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There's not really room to put the box on the landing of the stairs, which means the next stop after "just outside my office" would be in the main hall downstairs. I don't know if "steps" that involve it being out of sight (from the old location) work. There is also the husband factor...
I guess he just needs more time. (Giovanni, I mean. :-) )
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Or just wait. They really haven't lived with you for a long time, yet (ours seem to take 6-10 months to get settled in).
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2) Litterboxes should be in a place that is very easily and regularly cleaned. I really don't think you want to keep it in your office--I recommend the bathroom, and moving it there as soon as possible. Where did you keep it before?
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The shelter folks told me to isolate each cat in one room (separate) initially to ease the introduction to the house. That hadn't been my plan (I thought I could just open the carriers in the basement, show them the boxes, give them food, and count on them to come into the rest of the house), so that meant temporary boxes behind closed doors in two rooms, one of which was my office. Orlando got the idea pretty quickly so "his" room is back to normal. Now both of them hang out a lot in my office, but Giovanni doesn't want to come downstairs yet.
This morning for the first time he came out into the hall to greet me after my shower and then followed me into the bedroom, so that's progress, but when I tried to lead him downstairs he wouldn't do it. A few days ago he also wouldn't come out of my office on his own, so I'm hoping he'll be downstairs before too much longer.
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Which is why I suggest getting Giovanni to start using the one in the basement. Otherwise, you'll have a litterbox in your office for the rest of his life.