Song lyrics are poetic language. The language is often distorted to make the lines rhyme, to fit the rhythm of the music, or to create pleasing and musical vowel sounds. I know this song. I like this song. I don't expect it to make literal sense.
The phrase "a tunnel with a tunnel" is not a standard phrase. It doesn't have any clear, literal meaning.
The basic idea of the song is the feeling of being lost or trapped, with no escape, from dizzying, repetitive, obsessive thoughts. "Round like a circle in a spiral, like a wheel within a wheel."
I'm not at all sure I can put a literal meaning to "a circle in a spiral," either. "Wheels within wheels" is actually a stock phrase or collocation. It means "something very complicated." (It does fit the description of a piece of machinery called a "planetary gear movement.")
Railroad tunnels take you through a mountain. Darkness closes in all around you. Then you emerge into the daylight again.
He is saying that this is not that kind of tunnel. There's no escape. There's no exit. The tunnel does not lead you out again. It only leads to another tunnel, "a tunnel of its own."
The words suggest natural cave tunnels within a limestone cave. They branch and divide to form a three-dimensional maze or labyrinth. When you are in a long, complicated system of tunnels I do not know how you decide that you have come to the end of one tunnel and have entered another one.
As with the rest of the song, you cannot escape from the tunnel. The tunnel leads only to another tunnel, which then leads to an internal cavern.
A "tunnel 'with' a tunnel" fits the same general pattern of "a circle in a spiral" and "a wheel within in a wheel." You can't get out of the circle or the spiral or the tunnel, you just get further and further in.