Hi, Hattie, and the same tender wishes for you and yours.
We are fine, but older, and hunkered down from Old Man Winter, who hashas just now crept in our door here in Fort Worth.
Can't get a fix on your man's unit ID. Kids did"find a way" to slip in underage...it seems to have been a fairly routine thing to do.
Bob Cyne suggests that he may have been in the old CCC at the time, but that operation didn't come out until 1933, so I really don't believe that Bob's notion fits your 1931 photo reference.
As for a roster of deferred 4Fs, I doubt that such a list would be retained.There are records you can draw on which releal who registered for WWI and WWII, where and when, but these do not reveal what their individual classisfications were.
I will continue to cast about for some lead to your Telephone Detail reference...bet it tracks back to Old Army, WW I vintage.