Ammeter works when key is off?

"Fuse" is confusing.
It's not really a fuse, in the conventional sense, and it's best not to ever replace the fusible link with a conventional fuse. The F-link is a slow-blow device like Mattax said , and allows short term overloads, where a fuse would just pop and leave you stranded.
I think we're all on the same page, but felt the need to clarify "fuse".