A few months ago, the actress Sarah Paulson was at a restaurant in Los Angeles, waiting for a woman she had never met. She had spent weeks obsessing over her dinner date, even wearing the same fragrance.

“I remember her coming through the revolving door, and there was this dappled light coming through the windows, so I couldn’t quite see her face,” Ms. Paulson said. “But I had studied her physical mannerisms so much that I could tell by her walk and her hands, the way she was pushing. And then, of course, the one thing I could see was that mole, illuminated and kissed by the sun.”

In walked Marcia Clark.

They ate, ordered tequila and talked for so long that they closed the place down.

“The whole thing had this date quality,” Ms. Paulson said, still sounding giddy, as she recalled the rendezvous over lunch at the Four Seasons Hotel in New York. She felt “an incredible sense of kinship” with the prosecutor, whom she plays in the FX series “The People v. O. J. Simpson: American Crime Story.”