You are right Marvin, you have a bendix drive starter. Probably needs a little TLC. The procedure is in this section. Tells how to disassemble and clean.
http://chevy.oldcarmanualproject.com/shop/1934/34crm131.htm The manual says it is likely it's gummed up, but they were not thinking 86 years. So maybe broken spring or retainer or pinion gear. Gotta tear into it. Pretty easy. Old stuff is simple....but finding parts may be difficult.
The linkage drive/over running clutch style we thought you had, was in about 1938. Your motor could have had a "Starterator". Groovy.
I know very little about your starter. Phone call is out. We all need to see the conversation, then all can help.
