When MSCGR has the information, as it appears they have with my GGDad,
Arthur Sartin, you'll find discharge dates in the 3rd column, under Rank & Unit Enlistment,
Mississippi Confederate Grave Registry. That's where I found his, at any rate.

I haven't researched any Pension Histories, but they're likely to contain discharge dates too.
(I'm sure there must still be diaries and rosters in attics or antiquarian book shops, somewhere.)

Thank you, George - I will write (to MS Dept of Archives and History) and hope there
is more there on GGDad's record.