If you're one for quicker/shorter games, you're probably going to be hard pressed to see them.
I generally play 15 x 15, 11 - 13 Races, very slow Research, and I've seen then virtually every game.
They won't show up until later game, mainly because the overall Galaxy Tech level has to be pretty high . . . needs to be or you're toast
FYI, the "Beacon of Shaktur" won't show up until the conditions (Time, Tech, Galaxy Pop I think) are met.
This is probably why a lot of folks don't see them - by that time your Explorers are usually done searching.
If you're ~ 75 years in (guess), I'd open up the Galaxy map (lower right panel) and select "Ruins" and go through them. You may need to manually send an Explorer to investigate the Beacon.
First time I encountered them in testing I looked at their Military Rating and was . . . and that was before they were really PO'd
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