Hello Clementine, welcome to the forum and a Thank You to your dad for his service.
A typical Engineer Light Equipment Company consisted of 4 officers. 114 enlisted men.
They furnished supplementary equipment with operators to engineer combat battalions and operated as a replacement pool for construction equipment. Light equipment companies were attached to corps or army.
AmericanDivisions.com lists the 608th Engineer Light Equipment Co. under Army Engineer Troops for the Normandy invasion attached to the 1128th Engineer Combat Group along with the 1278th Engineer Combat Battalion.
The operation plans state that the 1109th and 1128th ECGroups will do general engineer work in the Carentan Peninsula area.
Later records of the 1128th Group do not list the 608th as being attached to them, so they probably went to Patton`s 3rd Army when it was activated in August `44.
I`ll try to find some record of them under 3rd Army later.
The 608thLECo has campaign credits for Normandy, Northern France, Ardennes- Alsace, Central Europe, Rhineland, and Occupation Duty, 2 May - 4 July 1945, Germany.