Not an answer, just some clues, perhaps, to the use, "to be noncommittal or inconstant".
Compare: wiffle-waffle, whiffle-waffle
The first (English Dialect Dictionary, Joseph Wright) gives a definition of wiffle-waffle "to whet a scythe", which I understand (perhaps incorrectly?) to involve a back-and-forth motion. Wright finds the attestation on page 141 of The Dialect And Folk-Lore Of Northamptonshire by Thomas Sternberg. London. 1851
Wiffle (whiffle) and waffle (whaffle, woffle) seem to involve swinging or swaying or moving back and forth (literal 'vacillation'); the word wiffle-waffle has among its meanings 'to speak in a meandering manner'. In the American use of 'waffling politicians', they either speak in an evasive manner so as not to be held to an opinion, or they flip-flop and say today the opposite of what they said last week.
The second instance from Dizionario Delle Lingue Italiana Ed Inglese, Giuseppe Marco Antonio Baretti, (1839), gives a definition for whiffle : to swing, to sway back and forth (muoversi ondeggiando...dondolarsi). [But this link was mere lagniappe :-) ]
See also whiffle-whaffle : "a person of unsteady, vacillating character" in
The Dialect of Craven in the West Riding of the County of York (1828).
