The legend of the "Deemster's Cairn" was collected from my great-grandfather by the late William Cubbon of the Manx Museum prior to 1932. The original white man apparently dated from c. 1770 when our ancestors constructed the wall. Supposedly this replaced the cairn itself which was there before. The whole thing got unstable, and was kindly re-built by the Manx Conservation Volunteers c1979 at our request.
As to the Deemster, if there was any truth in the legend, he would have lived & died long before death certificates & surviving burial entries - so who is to say.
Let he who can prove otherwise cast the first white stone.