Are you sure it was Army disciplinary action ... and not the church ?
Some Irish Catholic Chaplains got into trouble with their Archbishops after they came home ... because of the "Troubles" and all things to do with the British Army etc !!
When I was being taught History in school we were taught
some about the Easter Rising the War of Independence and the Civil War but practically nothing of the contribution made by Irishmen North and South to the First World War .... tensions ran pretty high when soldiers in uniform came home ... ( which is a whole other subject !!

)
Tell us what your historian said exactly .......... some stories have an element of truth but are not always definitely right !!

It's also possible he wasn't with a particular regiment ...
he was a Roman Catholic priest with the British Army !
Nice find Phil !!

PS This is a good site about Father Burke's 16th Division !!
http://freespace.virgin.net/sh.k/xvidiv.html