I think I can add something to the early story of the tambourine. It had a fanatical promoter around 1800: Joseph Dale (1750-1821), an organist in London who published William Shield's "Rosina". His enthusiasm led him to patent an "improved tambourine", which I think had a lever or two to change the tone. His compositions include a set of 8 waltzes for harp and tambourine
with accompaniment for flute and triangle, and a Grand Sonata for pianoforte and tambourine
with accompaniment for flute, violin and bass. (I've seen these. The tambourine parts look a bit like Labanotation).

My guess is that Dale was not unique, and there was a general vogue for the tambourine in Britain at the beginning of the 19th century. Maybe it was a spinoff of the "Turkish music" of Mozart's time, and maybe it came back from military campaigns in Egypt. Naturally it would have crossed the Irish Sea.