Re “Is it possible radar guys were in Army Signals, too?”
I would say yes based on what I’ve read in the official military histories of WW2 in the “Green Books”.
Radar specialists were in the Signal Corps (see if your father graduated from Ft. Monmouth, NJ SC school). They set up anti-aircraft radar units all over the Pacific, esp. where the Japs had airfields or carrier task forces.
Also used to pick up incoming US bombers and fighters who needed guidance to emergency bases, esp. on Iwo Jima.
My father-in-law was in an Assault Wave while others came in, possibly like your father, as detached elements to the Marines. Or perhaps your father was in an Assault Wave but after the beaches and shorefronts had been secured. Signal Corps men were not trained to be frontline assault troops but did fight when necessary.
They were electronics specialists - radio communications, radar, Forward Observers who called in target positions to both ships and land artillery, etc. They were the communications lifeline people for the Marines.
Very brave men.
He made a lifelong joke out of that connection.
Anytime someone challenged him on a technical issue, he would say, “Well, I studied at MIT.”
Post-war, he got in one year at Northwestern, but had to drop out and work full time when my older brother was born.