The regiment was not organized until 1864. It appears that Cash enlisted on Oct. 7, 1862, evidently in some other command. In April 1864 he was assigned to Co. "A", 1st Confederate Engineer Regt., going AWOL on August 31, 1864. He disappears after that.
Engineers are not armed and equipped for combat purposes, so there really should be no list of engagements, certainly not prior to 1864.