gone pecan n. a person who is doomed, defeated, or beyond rescue; a goner. Editorial Note: As noted in the 2003 citation, pecan is pronounced in this expression to rhyme with gone, so it’s something like "puh-KAHN" rather than "PEE-kann," which is another common pronunciation of pecan used throughout the United States. This expression is particularly common in Louisiana. Similar terms given by the Dictionary of American Regional English are gone goose, gone gosling, gone coon, and gone beaver. (source: Double-Tongued Dictionary)
Could it also mean gone nuts? After all, a pecan is one.
Sounmd like it would share roots with looking peaked? (Pronounced pee-kid. not piqued)
Etymology incomplete is just as nagging as not knowing the origin of the universe.  But here the why part seems to suggest itself:  it's how trivial one considers pecans to be, for their great profusions in locales of Louisiana.