This is a song of desperation; a song of communication that has broken down so much that the narrator, desperate as he is, really has no idea if anything he is trying to get across is getting through.
You don't have to be Marshall McLuhan to figure out how frustrating this is, and the narrator is practically driven to a nervous breakdown in just trying to say something to one Sylvia Avery, a woman he has loved and lost, presumably to the man who "lives down Galveston way." There is no deeper indication in Shel Silverstein's lyrics as to why Sylvia is leaving so quickly, only that she is - packing up, getting her umbrella, off in time to catch the train, all while the hapless narrator is singing. The operator (who is yet another stumbling block in the narrator's way) keeps demanding money, which means he's in a phone booth somewhere, feeding yet more dimes as he tries to at least say goodbye. But he doesn't get to do that; Sylvia's mom doesn't let him talk to Sylvia as she might start crying and thinking she should stay, and there's simply no time for that. I can see Sylvia's mom - perhaps a little old lady type, very nice but distracted; but overall protective of her daughter's happiness. That Sylvia is happy is the first stab in the narrator's heart; perhaps he knows she is with someone else, is engaged, or maybe has found out that she is leaving home and wants to say goodbye, and then the learns the news - he's history. There can be no rekindling here, no second chance. He asks and asks to have Sylvia hear his goodbye, to no avail - she's too busy. And so he gets her mom; a nice lady, nice enough - and this is the last straw I feel, for the narrator - to tell him that he can phone again when he likes, though it is highly unlikely he ever will. His whole purpose in life is this girl, this Sylvia, and she is disappearing from it, at great haste.
Anyone who has ever dumped someone will know how Sylvia feels. She is happy, and that happiness is so big that talking to her ex is literally too small a thing for her to do; she is washed clean of him and does not need his goodbye. Indeed even if it was the other way around, her new happiness eclipses any sorrow she may have felt, and his wanting to start anything up again would be met by a pity, a pity that only now, when he is losing her, is he trying to get her back. In any case she is eager to get to her new life and love as soon as she can, and has no time to be persuaded, to maybe feel different. There was a time for that, but it has passed; and so the hapless narrator (who has run out of change, or so I always think, by the end of the song) is left to cry and hang up the phone, walking out into that same rain, not even knowing if Sylvia herself knows or cares that he called. That he can't go see her in person - or didn't - is maybe an indication that seeing her again would be too much; the breakup wound is still too raw for him to handle. And now this. It is hard not to feel for him, and anyone who has called to get someone's mom or dad explaining that their son or daughter is with someone else will know the emptiness and scant consolation in that conversation. The narrator is desperate for one last word, but he gets the wrong female of the house; and so his hopes are dashed.
I will return to Dr. Hook & The Medicine Show in a few years - sadly with a song unlike this, but I will discuss that one when it comes. I should say that the songs I know by them best are the ones I heard growing up listening to Dr. Demento - "Freakin' at the Freakers Ball" and "The Cover of the Rolling Stone" - also songs by Silverstein and much more indicative of the band's genial strangeness and good humor, to be a kind of post-hippie band for the generation of those who were to grow up to be not yuppies but those determined to keep something of the 60s alive, however they could. That they would have their greatest successes once they lost their wackiness shows that the post-hippie generation somehow either mellowed out or began to focus on something else, something or someone more meaningful. (Even though Dr. Hook & The Medicine show were based in New Jersey, I think of that post-hippie crowd and Chez Panisse and Alice Waters come immediately to mind.) But for now, with Silverstein's songs, they are one facet of the early 70s, one that doesn't take itself too seriously, though with this song, they show they have heart; generations may come and go, but the pain of being too late to even say goodbye is a constant agony.
Next up: we like to be beside the seaside.