Unfortunately, none of my Ford documentation supports the OE production-installed reclining bucket seat availability for the '71-3 Mustangs. I've harvested a lot of parts from these era Mustangs when treasure hunting in the salvage yards "Back in the Day" and have never seen anything other than the standard fixed seat back.
If you want to angle your seat back slightly, try what Hemikiller suggested and trim the small circular black plastic washer/disc on the lower seat frame. Ford called it a front seat back scuff plate. I've had a couple of friends trim theirs down in an attempt to get at least a couple of degrees more in the seat back angle. On long rides or trips, they felt like they were sitting almost straight up and were very uncomfortable.
Although you stated you wanted to retain the original style seats in your vehicle, if you were looking for a reclining seat back choice and wanted it to meet current safety standards, a new model Mustang seat or an after-market version would be a better choice.
The first OE production-installed reclining bucket seat in the Mustang line was the '79 Mustang Pace car with the Recaro seats. They were so popular Ford made the Recaro seats an option in '80. In 1981 Ford made a non-Recaro reclining seat option available on certain interior trim levels.
As Hemikiller stated, people unaware of the automatic seat back release may have mistaken them and all the associated hardware for something else as these cars were worked on or parted out.
If you come across any Ford printed material about the reclining high-back bucket seats you referenced in your post, please share it with us. I'm sure many here, including myself, would also like to learn something new if documentation confirms those reclining seats did exist.
