Fear no more the heat o' the sun,
Nor the furious winter's rages
The familiarity with this quote from one of Shakespeare's most obscure works marks Spetimus and Clarissa as people of quality; they are not parroting "To be or not to be", or misusing the word "wherefore" as we could imagine the other guests might. Their shared moment is a more quiet, subtle one that can only shine and exist away from the people around them; for Clarissa, the line first surfaces in silence, in the absence of Lady Bruton's invitation, and for the last time when she is alone, away from her party.
Likewise, in The Mystery Guest, the narrator and his former girlfriend are linked by reading Mrs. Dalloway. This isn't in the excerpt we read in class, but the party they're at is filled with turtleneck-wearing, Dostoyevski-in-the-back-pocket-of-my-skinny-jeans-grade pretentious snots; amid all the windbaggery, the small line from Dalloway, "Roses were the only flower she could bear to see cut", describes a clear path between the two souls.
In neither case is the literary reference reduced to trivia; neither the narrator and his former lover nor Septimus and Clarissa are trying to gain street cred by showing off their knowledge, unlike the others at their parties, like Brierly who has made a career out of bloviating on Milton or the other guys at the fete, one of whom actually and inexcusably mentions Sven Nykvist.
In both cases, the shibboleth is silent or quiet; Clarissa and Septimus never meet, and the narrator in The Mystery Guest barely hears his girlfriend among the white noise of the party. In both of these works, so much of the speech is unnecessary, wrong, or misinterpreted. Holmes speaks a lot, but he doesn't understand much of anything. Jim Hutton can imitate Brierly, unsaddled by understanding, and the narrator's fellow revelers can and do titter away into the night without saying anything original. For the 'heroes' of our two works, literature, operating in silence, becomes the language of the link.