Tom Reid's list of deaths for the 13th Texas Cav. does not list a David E. Goodman as having died during that period.
There may be several explainations for this, such as exactly when in November that he died? He could have been in a Hospital in either Little Rock, or Pine Bluff, most probably Little Rock, at that time.
Capt. Clinton Fouty's Company "G" 15th Texas Infantry, lists:
Goodman, David E. Private, age 24. The Regimental Returns of November, 1862 (taken October 31st) at Camp Nelson, Arkansas shows him to have died.