There's an option to Research Geneology on the computer. This seemed to trigger it for me. I don't think it works if you already have a Stay Over in progress, or start one between researching and the event triggering, as the event itself (once triggered) is a Stay Over event.
For me it was a "Cousin" - They had Cousin RelBit, but didn't show in the family tree. Their surname/features matched my researching sim, but they had different colouring, so be sure to research with the household member you want them to be related to. They also had the Erratic trait.. So, it could be that they spawn with interesting archetypes.
