The Baseline Test in „Blade Runner 2049” is based off the book „Pale Fire” by Vladimir Nabokov.
In Pale Fire, the fictional poet John Shade sees a tall white fountain during a near-death experience – the image’s presence would always console him. Later Shade reads about a woman in a magazine who came close to death and glimpsed a „tall white fountain”. Shade finds the woman to share this with her, only to discover it was a misprint – it was not a „fountain” but a „mountain” that she saw. But the error changes nothing: the image of the tall white fountain had meaning not because it had some objective significance, not because it was empirical proof of an afterlife, but because Shade ascribed meaning to it.
With K or any other artificial being, you’re dealing with an entity that is inherently mentally unstable who don’t have the emotional/mental coping mechanisms endowed by evolution to natural conscious beings. These tests are, for lack of a better term, intended to make them „wig out” with word association – to attempt to discern even the most minute emotional reactions, such as brief pauses, fluctuating skin pigment, facial twitches, dilating of the pupils, blinking, or shifting of the eyes.
Pay careful attention to how long it takes him to respond to the questions. In the first scene, he pauses, as he’s asked whether he dreams about being interlinked (he does). In the second scene, he pauses several times and tenses up. The statements are meant to test his emotional response, and if he responds emotionally, he’s not fit for duty.
See also What means to be human?