The song Twilight Zone obviously gets it's name from the TV series which originally ran from 1959 - 1964, making it still on-the-air when Eugene wrote this song.
I want to give you a little bit of perspective about TV in those days.
This was before cable. There were very few channels and for all practical purposes there were only three stations with shows that people wanted to watch (nobody watched PBS), and even then, most of the choices were not that good. So when one of the three (ABC,CBS, and NBC) put on a high quality show it quickly became the show everybody watched and talked about.
Eugene was just jumping on a current popular show.
The trouble with taking on Twilight Zone as a subject to write about is that the show was not about one specific thing, so if you wanted to write a song about it your subject was that thing that tied all the episodes of the show together - weird imaginative stories.
Eugene came up short for both weird and imaginative .
The bar for what was weird and imaginative set by the show was extremely high, and Eugene gave it a shot but the best he could come up with was an underwhelming tale of someone meeting their childhood self. The story had few details and just wasn't weird enough to even get close to capturing the essense of the Twilight Zone.
Eugene was no Rod Serling, but I think he deserves credit for taking on suh a huge challenge in songwriting.