My guess is that we don't yet know what to look for.
If I had the resources, I would re-organize mass distributions of accretion disks near active galactic nuclei such that information was encoded into the jets of resulting radiation. Seems like a fun little prefabbed telegram station, of sorts.
Yeah, basically that's the idea. Problems: the jets are very directional, and don't point within the plane of the galaxy, so this would be intergalactic communication exclusively. Then there's the inherent chaos of the system that you'd need to overcome, but anyway... Like quite a few folks here, I think that we're looking for the wrong stuff anyways. Particle fluxes, EM waves, etc., it's all too classical. Maybe there's an ET signal ironically embedded in what we're calling quantum noise. This thread got me thinking even more though; If mathematics is the "language" of the universe, is it possible that there is some message embedded within our reality, somehow? We have multiple versions of string theory that may or may not be correct. As of now, most flavors aren't falsifiable with current experimental technology (crank dat LHC to 13.5 TeV). So what if we do eventually experimentally constrain our unified theories of everything to one model? Is that particular solution telling us something? "Interpreting" what quantum mechanics "means" has been a fucking nightmare. Accordingly, the metaphysical implications of a particular unified theory of everything will probably be infinitely more confusing. In fact, I'm going to stop typing and go cry now.