Could it be a belt of matter orbiting the star, with particles fluorescing?
The modulation period is 1.6*10-¹², the modulation frequency is 6.25*10¹¹. About the frequency of hard X rays. Could it be hard Xrays emitted by the star causing fluorescence in clouds of particles orbiting?
If this were the case, and we had the spectrum of the modulation, we could identify the elements fluorescing.
This could be a communication method between star systems. Put a cloud of something fluorescent into a decaying orbit around the star.