Hi Frank,
My Dad's records from the archives were disappointing because so much important info was faded-out, charred from the fire, or missing. He was in Company "A." You might be lucky but it does take at least four months to get anything. Otherwise, for specific information about your Grandfather, contacts through M1 and veteran John Fallon are the only resources I know.
The history of the 36th Engineers in context of the war is impressive. They spent more days fighting as foot soldiers (much of it on the Anzio beachhead) than building bridges or mending roads. They were among the first combat engineering regiments to enter the war and had one of the longest continuous records of service of any unit in WWII. The 36th Engineers made five major amphibious assault landings in the course of ten campaigns and were used so frequently as a shore party that they came to be regarded as Amphibian Engineers.
If you read everything about the 36th Engineers on this website and want to learn more in general through WW2 books, I would be happy to recommend some good ones. But rest assured that your Grandfather belonged to one of the finest units that served. Best of luck in your search.
Peanuts