I stopped by the airport today to take a closer look at a Beech B-18 (introduced in 1937). Walking up to the nose I could see flush rivets everywhere, but the aft end and belly were covered with shallow-dome-headed rivets, some quite small. The belly was especially interesting to me - the lines of rivets weren't all straight, giving the appearance of either a "saw horse" repair (wheels-up landing rash?), or intentionally jogging around some hidden feature, or perhaps it didn't matter much in that location? I don't know the exact year of this particular example, but suspect it was built during the war. I'll try to get photos next time I'm over there.
Please note that I'm not trying to imply that a B-18 was the source of 2-2-V-1.
The owner also owns a Lockheed model-12 that I am anxious to look at. Can anyone comment on commonalities between the -12 and Amelia's -10? Would there be anything useful to learn from studying a model -12?
I hope you can get access and learn and share all you can from this, what a great oppportunity.
The twin Beech is a near-contemporary to the Electra with somewhat similar construction (wonder where Beech got the idea...). It also enjoyed an extremely long production run - from around the time you mention (1937) until about 1968 if my memory is good. As such it was produced in many variant forms - and the flush riveting up forward may be a later effort that was not present on earlier models of the 18 (I do not know this - it can of course be found out).
If this airplane is in service then it should have an external I.D. tag - left side of fuselage, somewhere aft of the door (and possible tucked under the horizontal stabilizer nearly out of sight to the casual observer if a restored warbird, etc.). That would be the easiest way to get a full model and serial number so that vintage and other details can be determined. That might tell something of how the flush rivets got there (likely production of course, but question being was it cut-in for a later variant, or has the twin Beech always had that feature - I don't recall it on our old C-45's in A&P school).
As to the irregular rivet patterns - I'm not surprised, there are all kinds of reasons for that to occur - but most of them would have to do with 'post production'. As you mention, 'rash' from many things bring that about on many decades-old airplanes - and belly landings certainly occur, among other calamities (ask Ric, he's seen plenty of them as an investigator). Something could be learned if the records are there: oddly enough, repairs and modifications in today's world (since Federal Aviation Act of 1958, and possibly earlier CAA records as well) go into a public folder - forms 337 document major repairs and alterations.
Major alterations remain on record indefinitely ("forever") but major repairs may be dropped after one year - the presumption being that a proper repair 'restores' the airplane to an approved condition. That's a tall assumption on FAA's part because there's a wiggly line in there - very often a literal wiggly line: original fastener patterns often are altered. Not so bad - as long as pitch and size requirements are obeyed and within approved repair limits that's fine - but it can easily result in irregular lines as you see.
Of course an 'alteration' of some sort (a modification) can be the reason - but those are usually distinct, offset rows (and such could account for the offset we see in 2-2-V-1 compared to at least one museum bird. If you are seeing somewhat erratic rows then the suggestion to me at this point is you are seeing field-replaced skins that were hand-drilled into repaired flanges on belly members or perhaps replacement stiffeners, etc. It would not be the normal product of match-drilling to healthy, original stringers and stiffeners.
Interested in what you can learn from the L12, but it is a different (and smaller) airframe than the L10. On the surface they bear a strong resemblance, but I think there are many nuanced changes within the scaled-down structure that probably prevent it from being a direct model for us to consider. It is also a later model so some modernized features would be expected by comparison to the more antique L10. For one, look at the gear - there was an obvious advance in technology on the L12 over the L10 - the double-fork welded assembly is replaced by a forged, single-offset leg at the wheel.
I hope you can meet the owner and get a tour and his interest in some of this - great source of information.