I would doubt very much that Ford made an "spare tire carrier delete" for the '56 Birds. I say this for two reasons:
Number one, Ford discovered in early '54, prior to the release of '55 Birds, that the car had a serious design fault.. As the speed of the vehicle increased, the loading on the rear wheels changed from being positive, about 1,500.lbs at curb weight, to over 1,500 lbs of lift at speeds over 105 mph.
Two '55 Birds actually came of of the test tract, doing end over end flips.. Engineering tried to stop the release of the '55 Birds, sales over-rode engineering because they felt the majority of the '55 Birds would never achieve speeds over 100 mph.
A very famous auto designer Alex Tremlus, who I knew personally, the designer of the Tucker and other vehicles worked in the Ford design department at the time, Alex was given the job of redesigning the small Birds to overcome the lift problem. Alex' quick band aid was the rear extention of the bumper and the external spare tire, this counter balanced the car..
Ford marketing touted the removal of the spare tire from the trunk area as a feature to offset consumers complaints about a lack of trunk space..
Alex then redesigned the entire rear portion of the Bird which produced the '57, with the altered "fins and reversed slope of the truck" which is actually an early form of an air damn/spoiler..
Alex was a member of a car club that I was a member of for many years, he talked about his years with Ford at many of our club meetings.
The second part of the external spare tire issue is a '56 Bird that I have owned for many years. I'm the second owner of the car, it was bought new for a family friend, for her 21st birthday, Patti did not like the spare tire hanging out over the rear end, she had it removed.
This required the relocation of the exhaust pipes and the use of a front bumper in lieu of the original '56 rear bumper.. Basically the car now looks like a '55, except it has vents in the front fenders, which a '55 does not have.