I was much taken with the suggestion by Mr McGrath of the connection with Gay's Black-Eyed Susan, who cries farewell and waves her lily hand. All the time I have been reading thru this thread, the line as quoted in the Subject-frame has called to mind the moment in Chaucer's Miller's Tale where Alisoun has tricked Nicholas into kissing her 'ers' by sticking it out of the window where he expects to find her mouth. He, knowing that a woman "hath no be[a]rd", exclaims, "fy! allas! what have I do?" Then comes the line I have been reminded of throughout:
       "Teehee!" quod she, and clapte the window to"
Note the identical rhythms, with all the words but two in each case having single syllables, the 'and' appearing in exactly the same place, and the two two-syllable words, the first in either case an exclamation, appearing in identical points in the line, as does the second active verb in the simple past tense, 'clapte/waved'. Could there be any echo, however conscious, involved?