Whatever was done had to conform to approved practices. Aircraft repairs, then as now, were closely regulated and had to pass government inspection. The question I hope we can answer is whether there were approved repair techniques that would result in the rivet pattern we see on the artifact.
I wish you luck with this effort, whatever is being done to identify the origins of this metal panel. "Approved Practices" and vigorous inspection requirements certainly did apply and were taken seriously, so I personally doubt that an impromptu repair of lessor skin thickness and smaller rivet size would have been employed in an area of primary stressed skin (see
Airworthiness Bullitin 7H from the "Air Commerce Regulations" days of Earhart's time).
That does not preclude that 'anything is possible', or that exceptions could have been made, of course. I also understand and appreciate how the 'best fit' was determined by having read of the effort on this site, but have doubts about that location. This is due to the thickness (.032 being less than the original .040 skin in that area) and the irregular "#3" rivet hole pattern evident on the piece (which are also undersized compared to the 1/8th inch "#4" rivets originally used in that area of primary structure). For another thing, #3 rivets have long been considered less-than adequate for primary structure and generally are not used in stressed skin situations (this taught me from early days in A&P school, granted some years after Earhart's time - but a long-standing practice).
On the positive is the era of this 'skin' - the markings suggest pre-WWII production and the remains of brazier head type rivets also suggests an older craft, pre-dating the war-time AN470 universal-type head (both in terms of production and any repairs).
As to a 'likely fit' I am more biased toward the curious covering that was installed over the Electra's large, one-off 'navigation window' in the head while the ship was in Miami, prior to the last world flight attempt. This window was located on the right side of the fuselage - cut out and braced for a larger aperture than the other cabin windows, and actually placed in the lavatory area. This large window was in a zone of .032 skin since it was AFT of the station where ".040" skins stopped and .032 was the norm.
Of further interest to me is the general layout of the rivets - the interim "#3" rivet layout is as if done "free hand" by someone in a hurry to address an oil canning effect over a large, secondary 'cover'. What is 'suggested' by what I see is a rapid attempt to cover a large aperture simply for security / weather protection, but where structural considerations were not paramount; perhaps after a flight it was realized (or simply 'predicted' and addressed) that oil canning might be an issue: hence light-weight secondary rivets that could have attached light-weight stiffeners to prevent that.
Earhart was weight conscious; someone decided that window was no longer needed and it was covered while in Miami (details of that unknown). The larger rivet holes on the periphery of the 'skin' suggest attachment to established, well-braced structure (such as the peripheral bracing of the described window); the interior rivet patterns appear 'hand laid' and are light-weight in character, i.e. secondary consideration - weight savings but adequate for light bracing.
Of course all of this is speculation on my part - but based on the reasons I've given, which are based on a career in maintenance, alteration and design. The practices I've described are also consistent with the earliest guidance we have (
see the "Aeronautics Bulletins" of old on FAA's Regulatory and Guidance Library site), right through current sheet metal practices (actually little has changed in eight decades as to those practices except materials and fastener types, e.g. brazier head giving way to universal, etc.).
So in my thinking there is no way to know this for sure short of having NR16020 to hold this up against for an absolute match - belly or window covering, or something else - but the 'window cover' came to make sense to me after seeing the artifact in D.C. June of 2012 and learning something of the Miami window covering exercise, and more about the structure in that area.
Best of luck with whatever investigative effort is going on - I agree it is loaded with information, if it can be teased out somehow. I've always wondered if it might be a silent witness to this loss and somehow finally a key: there should not have been a great surplus of that kind of pre-war Dural with brazier rivets in it lying about in that part of the Pacific IMO, however it got there.