This is a rum 'un….
44tpi is not a standard Whit-form thread. Studying the Mechanical World Year Book 1957, and your supplied information, I reckon the following:
It's actually metric but not from the modern ISO Series.
So:… 7BA? BA is in fact metric, based I think on the old, Swiss Thury thread.
OD for 7BA = 2.5mm. Pitch = 0.48mm.
Enlarging the page to read the photo better…
Pitch by the rule: a gnat's crochet under 0.5mm.*
Dia. measured = 0.085 " = 2.16mm but could be accounted for by over-rounding when cut, and by wear in service. The thread does look as if it's seen a year or two.
So I reckon the nearest standard to the photographed screw is 7BA.!
'
(Long-time listeners to I'm Sorry I Haven't A Clue will know that unit of estimation…)