Greg Boehm tells me the cocktail does not appear in any edition of Patrick Gavin Duffy’s “Official Mixer’s Manual” previous to the Beard enlarged and revised version (my edition is from 1956).
Greg also reminded me that I had missed a silent “Comedy Romance” named “None But the Brave” from 1928. There are also two short films in imdb.com from 1912 and 1913 named “None but the Brave Deserve the Fair”.
So, as JCB suggests in his comment, we may never know exactly why this drink got named after this commonplace.
“The novels you mention are referring to verses gtom John Dryden’s St Cecelia’s Day Ode:
“None but the brave deserve the fair.” That is late 17th Century but the way it is used in the poem makes one think it was a commonplace saying even then. At any rate, the name of this one isn’t going to give you any clue as to when it became popular.”
I have to say, I still think it is odd that a drink with “Jamaica Ginger” shows up first in the Beard edited version of Duffy’s book.