Google (Camerapedia) tells me Kodak made the Autographic in the period 1914-1927. As you say, it look as if yours is a very late model. It surprises me to say patent information going back to 1902, long before this model would have hit the camera stores of that time.
The condition of the inside back cover metal on yours looks to be very good, BTW. About 800,000 were made. This surprised me. I had not expected so many, Box Brownies yes, but the Autographic was a mid-range market camera and not one of Eastman's el cheapo offerings.
You will have to replace the small round celluloid red window with a new one. I was once told these can be bought online. The window of my camera is pristine. I also have the box and the original instruction booklet, which as I recall is dated 1922. So this may be the date my camera was produced. Like in your case, mine was also a gift, it belonged to my partner's friend's mother who had it put it away in a closet for many years. When she passed on her things were distributed to family and somehow we ended up with the camera. A nice gift.
My mention of the China cabinet was not meant as a joke, BTW. I too intend to take my out one day, clean it up and put in on display in a same cabinet. When properly spit-polished (those old Kodaks respond well to a little TLC), it deserves to be shown off.
A little nostalgia here. I got into photography in Eastern Canada at age 14, in 1961 and for a few years I bought all my film and darkroom supplies from the now long-vanished Wilcox Photo Studio in Moncton, New Brunswick which I recall still had several of these new models for sale in a beautiful old Kodak display stand. How I wish I had spent some of my photo earnings (I did news photos and processed Verichrome Pan films for locals who wanted one-day processing) to buy one or the lot...