Can you provide a link to the second one?
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gambolerBooked solidto be booked solid is to have so many things on one's schedule that not a single extra appointment can be added.
gambolerthe context you asked forThere's nothing in that context to say whether Perry has a lot of appointments, so I'll just have to say that the definition there is the same as in all the other places I've seen "booked solid" used, which is as I told you about above.