Re: Drafted 1865?
Not sure about the draft.The "Report of the Adjutant-General of the State of Maine" lists 7 entries for a Joseph Johnson.The following should be your guy.
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Joseph B. Johnson, age 29, from Jonesboro, ME enlisted 3-1-65 in the Maine 15th Infantry, Company E.He died 7-7-65.
I do not have the "Report"; possibly it details others who were drafted, or they might just have been listed as enlisted.