Way back during the Vietnam war, gomers was a derogatory term for Vietnamese. The USAF being more than a little slow to acknowledge the need for Dissimilar Air Combat Training, waited until after our involvement in SEA to start DACT. During my time flying in the USAF (79-89), Gomers referred to Aggressor pilots. AF pilots that had flown a tour as an Aggressor pilot would refer to it as, "I was a Gomer at Clark/Nellis/Alconbury." A co-worker bud that was an F-14 guy and later an Aggressor at NAS Fallon recognized the term. He didn't refer to his experience as being a Gomer, he described the assignment as, "I was an Adversary."
Gomers/Aggressors/Adversaries lived and breathed air-to-air combat. Every one of them became a SME (Subject Matter Expert) on some aspect of a potential enemy's air defenses. You can imagine, it was a coveted assignment. But an extremely demanding one too.
If you've read
Sea Harrier Over the Falklands you get the wrong impression of the Gomers job. Ward painted his training with the 527 TFTAS from RAF Alconbury in unflattering terms. They weren't there to beat your d*ck into the dirt, they were there to train you by flying like the enemy. They were a lot of fun to fly against!
I never heard anyone broadcast the term Gomer over the radio. I only heard, Bogey, Bandit, and then with a Visual Identification (VID) aircraft type (F-4, F-5, A-7, etc or Phantom, Eagle, Hornet, MiG, Flogger).