Problem is, a star is curved, with the limb being over two light-seconds farther away from an observer than the center. Sure, you can switch the whole surface of the star as fast as you like, with bandwidth limited by how accurately you can synchronize the switching components. An advanced civilization might be pretty good with attosecond-level stuff, but the signal gets spread out over seconds regardless of the synchronization superscience you apply.

You can phase the switches and "aim" the star's signal at a point in the sky. Lower-frequency modulation can get signals to observers not on the direct line, at a lower bandwidth, and you can probably sweep these. Worst case you can blink the whole affair slowly; a star with a five second light curve is going to be pretty interesting.