Since secession requires "mutual consent," meaning the approval of Congress, the Deep South could legally have sent emissaries to Congress to seek its approval and establish whatever terms appropriate.
But of course, they never wanted to secede legally.
What they wanted was the same as our Founding Fathers -- a Southern Revolution, to win their freedom and independence on the battlefield of honor.
Therefore, the Deep South sent its emissaries to negotiate not with Congress, which could deal with it, but with Lincoln's administration, which had no express Constitutional authority for it.
Or am I mistaken?
Did I miss that part in the Constitution which says the President can negotiate terms with rebels and insurrectionists?
Since the USC is TOTALLY silent on secession, the concept of legally seceding is moot. We've been over this many times here, maybe it one day it will sink in.