GEM/Ever-Ready Handle Adapter

Rereading my post, it makes no sense. I'm trying to find out about the thing that threads in to a standard razor handle and the 1912 head.
 
 
You're a scholar and a Gentleman! The link out doesn't work bu ifmve found some 10/32 grubs on eBay. Do you reckon 5/16" (~8mm) will be long enough to mate the handle and head?