[Jim McDougall]

The term (= seek and ye shall find) is from the mysterious inscription on the green flag (of Florentine soldiers defending Siena in the Battle of Marciano) in the fresco by Vasari.

I found this "The Paternoster Blade" by Chris Laning, in the Paternoster journal Jan. 8, 2008, in which this 'curiosity' which has been piqued in me seems to have affected others as well.
It is noted as a reference in Stone's huge compendium of 1934 describing the paternoster on sword blade phenomenon, and citing Burton (as I have noted) 1884, p.136 as a source.

The author here describes the fallibility of Victorian scholarship and also suggests that Burton, seeming to be the key source to this notion, likely saw this referred to and elaborated accordingly. While the practice of using the blade decoration as described is unlikely , here another Victorian myth was born.