Hi Chris, welcome to our forum.
You`ll find a lot of information on the 405th Engineer Water Supply Bn. in the document: "Engineer History, 5th Army, Medditerrenean Theater" availably in the documents tab on the main page.
What they did & where they were is given in the unit operations sections.
From Appendix H. unit histories:
"405th Engineer Water Supply Battalion
The 405th Engineer Water Supply Battalion was activated at Camp Breckinridge, Kentucky, on 20 November 1942
from a cadre supplied by the 85th Engineer Heavy Ponton Battalion.
From the time of activation until 1 May 1943, when i t moved to the staging area at Camp Patrick Henry, Virginia, the battalion
was busy organizing and training. On 10 May, the battalion departed from Hampton Roads, Virginia, for overseas.
It arrived at Oran on 23 May, and was assigned to the Fifth Army s ix days l a t e r .
Headquarters, Headquarters and Service Company and Company "B" were attached to the Atlantic Base Section at Casablanca,
French Morocco; Company "C" was attached to the Eastern Base Section at Bizerte, Tunisia; and Company "A"
went to Oujda, French Morocco. The period from the time of arrival overseas until the initial landings
by the Fifth Army at Salerno was spent in securing equipment, further training and normal water supply operations."