But guarding fumes and making haste
It ain’t my cup of meat"
It's clear we need to figure out who this person is, but the answer to that question isn't nearly as clear as the question itself. He seems to be a member (maybe the storyteller) of a small group who are collectively awaiting the arrival of this Quinn person. This is not unlike Vladimir & Estragon in Waiting for Godot. We have a group anxious to see the arrival of some sort of leader/savior, but it's quite possible that this person will never actually arrive.
The Mighty Quinn's deferred arrival seems clear in the following line as our speaker derides the practice of making haste, as if to imply the people can't rush Quinn's arrival; he will come when he comes. Here he reassures the group as if they are getting antsy and possibly even starting to doubt. We have a speaker maintaining and even reinforcing his faith in the face of the non-believing masses. Here he breaks with the very masses he seems to side with in the previous line which again suggests that he isn't as willing accept the idea Quinn may never get here. Just like Vladimir and Estragon, he holds tight to the dream. Unlike them, though, his dream is more ambiguous. Whether or not Quinn will actually ever arrive isn't quite as clear. In typical Dylan fashion, the meaning shifts from listener to listener and even from listen to listen for the same listener.
And finally, we get to the humor. After the claims about haste, he explains that making it ain't his "cup of meat." On the surface, this seems like a word choice designed solely to meet the rhyme scheme, yet there may be more to it. While measuring meat by the cupful isn't very common, perhaps it's a standard unit of measure in the community of Quinn followers. This doesn't seem like a useful standard though, because different meats demand different weights to equal a cup. Then again, when the more common "cup of tea" claim is made, it's not weight that's being discussed, but rather personal preference. It's not the speaker's preference to rush, just like he suggests Quinn also recommends taking it slowly. For instance, once he gets there, everyone will want to "doze" or rest. We see the speaker really giving the same advice as Quinn will give. The irony is that he has arrived at the message of Quinn without Quinn. This ultimately leads to a decentered and deconstructed messiah, and if they can arrive at his teachings without him, we see that the savior isn't needed. "Doing like the rest" is presented then as a bad policy since the real meaning can be found within the individual. A sort of Ralph Waldo Emerson meets Dorothy Gale meets Tommy Smothers. When you go looking for your weird, acid induced cup of meat, you won't have to look any further than your own back yard.