John Harris proposed a radical solution to the KIC 8462852 problem: it is a Halloween pumpkin.
A full Dyson sphere does not have to be 100% opaque. It consists of independently orbiting energy collectors, presumably big flat surfaces. But such collectors can turn their thin side towards the star, letting past starlight. So with the right program, your Dyson sphere could project any pattern of light like a lantern.
Of course, the real implication of this is that we should watch out for trick-or-treating alien super-civilizations. By using self-replicating Bracewell probes they could spread across the Milky way within a few million years: they ought to be here by now. And in this scenario they are… they are just hiding until KIC 8462852 suddenly turns into a skull, and suddenly the skies will swarming with their saucers demanding we give them treats – or suffer their tricks…
There is just one problem: when is galactic Halloween? A galactic year is 250 million years. We have a 1/365 chance of being in the galactic “day” corresponding to Halloween (itself 680,000 years long). We might be in for a long night…