For ungating appeals, the “case” you’re working inside is just a normal Amazon support case in Seller Central, but it becomes the container for all back‑and‑forth on that specific approval request.
The Case ID itself is a long numeric string (for example, something like 18499193641), usually shown in the subject line of the email Amazon sends you and in the “Case log” section of Seller Central under Help → View case log. When you respond to an ungating denial, you should always reply inside that same case instead of opening a brand‑new one, so the reviewer can see your previous documents, their prior notes, and your updated invoices or explanations together in one thread.
In terms of timing, Amazon typically expects responses within about 14 days; after roughly 30 days of inactivity, cases are often auto‑closed and you may need to start again with a fresh application. A practical approach is: reply with your updated documents and short explanation within 3–7 days of the denial, then allow a few business days for review before following up again if there’s no new response logged.