At the end of part 3, McMurphy and some of the other patients are driving back to the hospital. On their way, they pass by the house that McMurphy used to live in when he was a child. McMurphy stops the car to take a look at the house, and he spends a few moments reminiscing about the past. Soon, his attention is caught by a dress caught in a nearby tree. This dress reminds McMurphy of a moment from his childhood when he was "about ten" years old, when " a girl took him to bed for the first time. He recalls that at the time he thought that "if you made it, man, you were legally wed, right there on the spot." This is an important memory, and an important moment in the story, because it helps to humanize McMurphy. Kesey ultimately wants the readers to sympathize, or at least empathize with McMurphy, and he makes this much easier for the readers by giving them this glimpse into McMurphy's childhood.
This moment outside McMurphy's old house is also important because we are given a glimpse of McMurphy's real state of mind. It so happens that "a set of tail-lights going past" lights up McMurphy's face for a brief moment. In that moment we, through the narrator (Chief Bromden) see that McMurphy looks "dreadfully tired and strained and frantic." This is not ordinarily a face that McMurphy would allow the other patients to see, and if they catch a glimpse of it in this moment it is only because McMurphy "figured it'd be too dark for anybody in the car to see." In this brief moment the reader may understand how much of a strain it really is for McMurphy to fight all of the patients' battles for them. He usually puts on a brave face for their benefit.
As far as we know, Chief Bromden is the only one of the patients who definitely sees McMurphy's "tired and strained and frantic" expression in the tail-lights. This is important because it proves to Chief Bromden that McMurphy really does care about the other patients. This is perhaps the moment when Chief Bromden's love for McMurphy is validated, and compounded, and it is also a moment, therefore, which perhaps motivates Chief Bromden's dramatic show of love for McMurphy at the end of the novel.