Freeing up space · Recycle Vault
Is the Recycle Vault stored on my Mac or on the external drive?
Short answer: The files live on your external fast drive and your Mac keeps only a small list, so clearing really frees space. With no drive connected, items wait on your Mac within a size limit and move across when you reconnect.
Your external fast drive holds the files; your Mac holds only the list. That's deliberate: if removed files stayed on your built-in drive, removing them wouldn't have freed anything.
The list is tiny, so the window can always tell you what's recoverable and which items need the drive plugged in to actually bring back. When no drive is connected, removed files are held on your Mac temporarily, within a size limit, and moved across as soon as you reconnect.
The window says this itself: its settings have a Where it's kept section, and the vault's size at the top can open it in Finder. See does it need my drive.