Hey there,
Dig a LOT of digging and wrecking my nerves about this after completing all of the 12 annals when Archivist Inkforge was nowhere to be seen for the last 4 days in the order hall.
The solution that has worked for myself, and reportedly several other people is put place all of your artifact weapons into your bank and go back to your order hall.
To test this I went back after completing the hidden artifact appearance to the bank to grab my artifact weapons and he despawned again…
First time posting, so can’t attach visual proof, but feel free to try it out and bump if it works for ya’ll too <3.