I think the watch you linked is the Glycine Airman GMT. I believe the standard hour hand actually has a 12-hour sweep (yes, even though the labels are both 24-hour) and only the GMT hand (pointing to the 10) has a 24-hour sweep.
From what you've described, you probably have the Glycine Airman Purist [1]. There is no GMT hand but the regular hour hand has a 24-hour sweep (and you can set the second hour dial).
(I also have a Purist.)