I've been searching for stories on sentient electricity or other electromagnetic radiation. I've found a lot of them so far, but none of them except one match the descriptions of any form of EM energy attaching to people's heads.
And that one is about a halo of light attaching to one man's head. (And near the end of the story, his wife's head.)
So it's the closest match, but I'm still not satisfied. It's "Variations of a Theme" by Curt Siodmak.
An American couple is visiting Rome, and the man just suddenly sees a halo of light around his head. He cannot get rid of it. They are in Rome, touring every church, after all, so even the physicians and prostitutes he seeks out get frightened and shout "It's a miracle!" and fail to help.
He starts acting out several of the seven "mortal sins" on the idea that if it is some kind of mystical saint thing, acting out the sins would get rid of it.
What brings it into the "fantasy and science fiction" genre (more fantasy) -- besides being published in the Magazine of Fantasy and Science Fiction June 1972 -- are attempts by other characters to explain it:
"I'm in the small-appliance business. I know an electric aureole when I see one."
and
"The Edison Company," McWilliams said resourcefully. "They might use him for advertising their product. After all, it looks like it's being created by electricity."
There are no other people (besides the man's wife) who get this phenomenon, and there are no narratives of it emanating from any electromagnetic sources.
So this story is simply the closest match so far. I'm hoping that this one will lead to answers somewhere that include variations on that theme (ha) and that lead to an exact match.