My white whale would be the one Frusciante has, with engraved hump inlays but also FilterTrons.
Is the serial number of that one known? I think it might provide some insight into just how slowly and piecemeal Falcons were produced in the '50s and early '60s. Compare it to the one Jimmie Webster was playing in that '57 NAMM video. That one had blank cover FilterTrons with smooth surrounds, a vertical logo, Melita bridge, switches parallel to the neck, and thumbnail inlays. This one has a mix of one even earlier feature (engraved humpblocks) and other later features (angles switches, sculpted surrounds and presumably PAF covers). It would seem to suggest that Gretsch must have been slowly assembling and finishing that first batch of FilterTron Falcons with mixed and fluid features for the better part of a year.
It just occurred to me that Dan Duffy's remark about how much production employees hated building Falcons may well have something to do with how they were produced. I think most people would agree that when you have a task that you hate doing, you only do it when you need to. So rather than building nightmare batches of Falcons, they simply set aside a range of serial numbers and only completed Falcons as orders came in.
Damn, November has been a good month for my habitual speculation. First I definitively solved the double label mystery, and now I have ascertained beyond a reasonable doubt why early Falcon production was so sporadic and full of mixed and lagging features inconsistent with the serial number ranges. Well, to my satisfaction, anyway.