On the Tishomingo County MSGenWeb there is a transcription of the "Enumeration of Confederate Soldiers and Widows" for the year 1911. On this enumeration there is listed J. H. Good with the following information:

Name: J. H. Good
State of Enlistment: Mississippi
Company: E
Regiment: 2
Age:79
Year of Enlistment: 1862

This transcription can be found at the following link:

http://www.theusgenweb.org/ms/tishomingo/1911soldierswidows.html

Also, have you searched for a pension application file? There is a possibility that your ancestor applied for a Confederate Soldier's Pension. You didn't mention having searched for one.

Regards--