The most plausible explanation that they could be fully invisible but chose not to be I've heard so far is from Robin Hanson, but there are several parts and that alone lowers its probability. Still, fun to think about, and also addresses things like how they could be here/find us at all, why are they here, what do they want to achieve. I'll risk a summary rather than just linking out... First they would be pan-spermia siblings from our stellar nursery, so they evolved in the same galaxy and could find their stellar siblings among all other stars. They're many years more advanced than us but for some reason they have a strong norm against expanding and rearranging our galaxy and beyond to their desires. We're still around so they don't want to wipe us out without reason, but we can guess that if we get ideas and capabilities of becoming grabby, they're here to nip it in the bud. Being sort of impressive but also mysterious can eventually let us know they are there without revealing too much since we could easily collectively find something out about them to hate and think of them as enemies. If we admire them instead we're more likely to try emulation including adopting a norm against spreading out to the stars as fast as we can before even more matter becomes unreachable or some other aliens from farther away galaxies arrive here in several hundred million years.

One benefit of this explanation is it predicts we'll see more of these strange phenomena even as our technology gets better and the possibility of simply being mistaken is driven way further down. If we stop seeing them suspiciously around the same time as big advances in sensor and sensor integration tech, all the more reason to bet on old observations being mistaken/hoaxes/conspiracies than actually aliens.