Mutants aren't just found in the comic books and movies; they're also in Toobworld. Earth Prime-Time had at least one TV series about Homo Superior - 'Mutant X'. ('Heroes' may have been about mutants, but they could also have been about mutates. Mutants are born that way; mutates are genetically altered later. Beast of "The X-Men" - now a resident of Toobworld thanks to a Farmer's Insurance blipvert - is both. Anyhoo, after Future Hiro met Peter Perrelli on the subway, the timeline was changed and the rest of the series ended up in a parallel dimension. So if there was anything to that stuff about their powers being triggered by an eclipse later in the series - I dropped out partway through Season Two - then it wasn't really relevant to Earth Prime-Time.)
'The Twilight Zone' had at least one mutant - Jimbo Cobb, a simple man with the power of telekinesis. And even Claudette Colbert played a mutant, in an episode of 'Suspicion'.
"The Last Town Car" told the story of Edith Miller, who thought she was being haunted by an old-fashioned taxi. Whenever she rode in it, she was transported back to a crime connected to the cab some decades before.
It turns out she had psychic abilities and was actually tapping into the memories of the cabby. Many years before, he was the personal driver for a spiteful old man who ruined the lives of his own two children. The driver couldn't stand to see him hurt anyone else and so he pushed his boss into the oncoming traffic. As he thought back on his crime, the scenario was replayed for Mrs. Miller as though she was actually there to observe it.
I don't know if either Jimbo Cobb or Edith Miller can blame an eclipse for their abilities; I think they were born with those "talents". But based on the ages of both characters, mutant abilities pre-date the dawn of the atomic age....