but, bill, the phrase may predate WWII; the air force was originally part of the army.

but. this is from the American-Australian Slang Dictionary (online):
get on the stick phrase. (from the early 1900s, referring to starting to move a car by putting it in gear with its gear-shift stick) Begin working
http://psy.otago.ac.nz:800/r_oshea/slang.html#G