Data point for anyone arriving in the late evening after the TWOV desk closes - if you're on a tight schedule after arrival, it's not a good idea to do so. While you will ultimately get the stamp and be on your way, it could take 20-30 minutes depending on which primary inspector you get and their familiarity with the process.

My inspector needed to find the TWOV stamp (they had only one and it was floating around the room somewhere), then send my file to the central control desk so they could call the onward airline and verify my ticket....and ultimately the central control desk took over and finished the stamping and documentation.