I haven't read all the posts concerning this but a few suggestions

Start at LAST known county/state, try to locate cemetery surveys online or in book form, MANY online postings of cemeteries are INCOMPLETE so don't assume if you view some that he is NOT there. search this county AND BORDERING counties, many times in county creations the borders change BUT the persons/cemeteries/churches are in the SAME PHYSICAL location.

Go to rootsweb.com, choose the county location board and the surname board, post request in BOTH, put in subject line something short and defining like

NEED GRAVE location of Civil War Vet Patrick L. McCawley
or something like this narrow down subject line to time period (civil War) and looking for grave, this alerts those who may SPECILIZE in either, after you check THOSE counties postings/searches then try to locate LAST KNOWN stste/county of his siblings/wife etc, do same with these locations, he may of been buried with them.
DON'T assume he DID DIE IN WAR AS RECORD SAYS, check census index records for states involved AFTER war period, his body may of been misidentified on purpose or by accident, he may of took up new life elseware and would show up in records latter. Just a few ideas