This one has me stumped...
The spline count on the stem would help, but it looks like square universal repair handles have been installed in the past. Doesn't look like a Standard, maybe a Phister or Central from that era. Sometimes taking a photo to a plumbing supply house or hardware store that has older repair parts would lead you in the right direction.
John is usually very good at these, let's see if he stops in to the thread.