Don't remember any in TV shows, but many movies are based on Vietnam Vets.
Movies would have nothing to do with light TV fair, but do you notice why Vietnam vet is used in the movies, it isn’t used purely for patriotism, or for lightheartedness, it is always used to brand the character, as a psycho, or possibly unsafe, or to indicate his ability to fight. A beloved and sweet grandpa or dad in a movie or sitcom could always be a WWII vet or a Korea vet.
Even in light hearted TV shows a man could be a WWII vet or a Korean War vet, but Vietnam vet is too dark for sitcoms and sitcom like, cartoon shows.