Great explanation taken from someone on a different website
I think Miles Davis was the sound that these kids were listening to in their youth. The Jazz musician, by say 1959, had been well into his career. So to hear Miles Davis playing on a record or "on grandmama's radio" would bring back a flood of memories and nostalgia about this person (girl) who has wandered from him as they have grown older. "My have the years of our youth passed on" seems to mean that they continued a relationship of some kind into the future though, as predicted, she wandered.
The album actually deals quite heavily with concepts of memories/nostalgia, among others, but also abandonment. The yearning for this person to return leads him to plead for her "not take too long to come home."
And in Great Expectations we see something similar when he sings "I saw tail lights last night in a dream abut my ex-wife." He has been left again, perhaps by the same person.
In the '59 sound, he is left alone yet again, and permanently, by someone dieing in a car accident. I still have to look further into other songs to see this particular theme pop up.
Hmm...
...I'm actually starting to think that the "someone" in each case is all the same person, perhaps stretching across the album as a whole.
In this song, it is his child hood friend, who he mentions in The '59 Sound, as the person he "knows 'cause we were kids and we used to hang." Only to grow up to become his lover or spouse and be the leaving "ex-wife" mentioned in Great Expectatoins. She is the one who dies in a car crash, going "down, down, down, from [her] youth to the ground." And she plagues him in his dreams causing him to "wake up sweating in my room."
She is to forever be the recipient of the singer's longing who hopefully, and pitifully, leaves the floodlight on as a beacon for her return.