Thanks for that video, I think that this gun does have a military history.
Robby I tend to agree with you about the engraving from the stand point if the engraving is done at time of manufacture. This appears to be done by a layman, maybe an armorer that had to put a rack number or ID number for some reason after manufacture. The engraving on the barrel is also very modest and plain, not bold as we are accustomed to seeing on German guns.
Was the town of Neustadt in Germany during the late 1700's & early 1800's? Maybe a military presence for the town of Neustadt? Is the name on the barrel the maker or owner? Enquiring minds want to know. The great condition that this gun is in is probably due to a military history. It was well care for and the fact that it was apparently made pretty close to the end of it's use as a military weapon, according to the video, probably is another reason.
I am getting an education here!