From the Middle Ages to the 19th century, drummers led the infantry to the battlefield (see wikipedia.org, Tambour Major). Since Dylan begins the first verse with "though I know that evenings empire has returned into sand, vanished from my hand ..." it is hard to believe that he did not have this role of drummer in mind.
But who is the narrator in the song?
Well, one of the nameless soldiers who went into battle with the tambourine man. This is now over (see beginning of the song), what remains is a partially destroyed world (the ancient empty streets to dead for dreaming) and the former soldier feels anything but good. His weariness amazes him, he is branded on his feet and after all, he has no one to meet. In this situation he remembers the tambourine man, in which he apparently trusts and also expects help, after all he has led him safely through the chaos of war. He turns to him by calling him with "Hey Mr. Tambourine man play a song for me ...".
However, the horrific events on the battlefield left deep marks on the nameless soldier - he is traumatized. He is not able to perceive his normal environment, he is only fixated on the tambourine man who is physically no longer available (the war is over). Nevertheless, as in the warlike past, this should solve all his problems. At least that's how he remembers it. An effective means of survival was a retreat in time, a kind of coordinated escape. In the next 3 stanzas we are confronted with various types of escape.
For this purpose, a trip on the whirling magic ship is addressed in the 2nd stanza (take me on a trip upon your magic swirling ship). Quasi as an emergency measure. Because our soldier still suffers massively from physical and mental problems. All his senses have been stripped, his hands can't feel to grip and his toes are to numb to step (they need the boot heels for wandering). He promises the tambourine to go anywhere (I'm ready to go anyhow) and to submit to it (I'd promise to go under it).
The third stanza brings an approach to trauma coping. The nameless soldier processes his war experiences in a modified form. He projects his modified memories of what happened onto the firmament. There he thinks he can hear a crazy laugh which can be heard around the sun. However, this does not represent a danger (it's not aimed at anyone), it just slipped out on the run. It is also easier to escape because there are no fences in the sky that could make the whole thing more difficult. Even the fragmentary rhymes to be heard, matching the beat of the drum, come only from a ragged clown chasing a shadow. So a bizarre but less dangerous scenario than it was back then in the warlike reality.
However, our soldier still has a long way to go. This can be seen in the fourth stanza where he is toying with the ultimate way of escape, the disappearance. For this, too, he sees the Tambourine man as the ideal protagonist. In contrast to verse 2, this time it is not a matter of a physical escape, only a change of location would not change anything in his worries and mental well-being. Since a trauma is primarily anchored in the head, the starting point for its disappearance should be found there (take me disappearing through the smoke rings of my mind). Ultimately, what matters to him is to escape the stranglehold of these crazy worries (the twisted reach of crazy sorrow). And, if that (this time) is not yet possible, at least forget his memories and fate until tomorrow (let me forget about today until tomorrow).