As far as I have been able to discover over the years, and being one of the very few to own such an instrument, hence the interest, the parts were acquired from dismantled and/or damaged Thunderbirds, from several JAE bought up at the time he started using them, and iirc he asked Peter Cook (who I believe was a WHO roadie, or at least "inner-circle") to build a Precision thickness body (mahogany, afaik) in the Thunderbird style - tail/bridge/pups were all Gibson, the neck was a "D" profile Precision... the bridge was positioned 1/4" forward of normal to those on Gibsons at the time...
My Peter Cook Thunderbird was almost certainly built at around the same time; and although she has a through neck (with a "D" profile) and has some original Gibson components (tail and bridge) does not follow either a Gibson Thunderbird or a Fenderbird in construction: just a Fender profile through neck with a Thunderbird shaped body...
Mr Cook is not available for discussion...