Surprised this wasn’t already here (but knowing my luck, the usual hawk will pounce with the dreaded "Duplicated" posting very shortly!)
My posting derived from Ibiblio Fiddler’s Companion, which also has these notes:
GIN YE KISS MY WIFE, I’LL TELL THE MINISTER. Scottish, Pastoral Air (4/4 time). A Minor. Standard. AAB. "Very old air." This was the original tune for the Sean Trews/Triubhas, an ancient Highland dance in which the dancers wear tartan trousers rather than the sporran and kilt. Source for notated version: Mr. “Old air. Communicated by Mr. John Stuart” (Keith, Banffshire, Scotland) [Skinner]. Hardie (Caledonian Companion), 1992; pg. 50. Skinner (Harp and Claymore), 1904; pg. 59. Skinner (The Scottish Violinist), pg. 21. Culburnie CUL110, Abby Newton – “Crossing to Scotland” (1997). Maggie’s Music MM107, Maggie Sansone with Ensemble Galilei - "Music in the Great Hall" (1992).
At least yours has the correct key sig (it ends on E but it’s in A minor).
There are LOADS of historical versions of this, and it’s even just discernible as the Shetland D major reel. Some of the oldest versions are in D minor. A sketchy version, which Alasdair Fraser used as the starting point for a long exploration, is one of the ‘Skye Dance’ tunes from Patrick MacDonald’s ‘Highland Vocal Airs’.
Best wishes from "not ‘the usual hawk’…"