I had scanned the CSR, but had not seen the diagnosis (nor was my allusion to the rise and fall of his career an intentional pun). I had thought perhaps drinking was his problem. (Surely, given A.P. Hill's youthful record, per Bud Robertson, he would not have cast the first stone.)
There had been no lieutenants in the "regular" Signal Corps until the legislative ceiling was lifted in Sep-Oct 62, so Burke would have been among the first -- making me think that, like others, he had caught the eye of a senior officer and/or had experience in signaling. Whether his training was OJT or direct, I'd expect it came after Oct 62, notwithstanding the May 63 date (which could have carried him to Gettysburg, yet no commutation of rations chit got into the file to put him there).