While not a necessary thing, I would be most intrigued if it turned out that electromagnetism, like gravity, could have a time dilatory effect. The thought crossed my mind the other day, and it has
crossed other peoples' minds on occasion as well.
The consequences if such an effect were found would be profound: it would take gravity out of the running as the sole arbiter of time dilation and either expand or nullify the Equivalence Principle. "Spacetime" would have to be modified, since electromagnetism has a differential effect on particles that gravity does not.
The effect might turn out not to exist, of course.