I shared a lab with an instructor at my university who made photovoltaics that absorbed the non visible spectrum but allowed visible light to pass through.
I'm sure these are thought of already but I don't know how/if they are looking for all of these
* Absence of a star (fully engrossed in a Dyson structure) -- this seems like how a black hole.would be identified by circling bodies around nothing
* A visible star, but it has some part of its em spectrum clipped because it's totally encased by a sphere that only absorbs a portion of the em spectrum
* The Dyson sphere is large enough to encase many galaxies (including us)
* there's Dyson sphere s but they don't rotate so we don't see any sharp change in luminosity
* There's a binary star, but one is a Dyson sphere and appears as a planetary body