Nor do I find the surname Bresler in any Confederate units. S&SS has a Jacob Bresler in the 20th Regiment, Louisiana Infantry.
Are there any variants in spelling of the name Bresler?
I did find a partial roster in the NPS SSS, however, I cannot locate any of these men in the CW Research Database
George Martin
TRIGG'S BATTERY, ARKANSAS ARTILLERY
[NPS Soldiers & Sailors System]
Private George W. Anderson
2nd Lieutenant/Drillmaster William Norman
J. S. Parsons
J. B. Parsons
Private Jas. Shehan
Captain John T. Trigg