Vivienne Eliot gave her husband a mandolin when they went to Margate in October 1921. This was when Eliot was on leave from Lloyds Bank to recover from a case of nerves. After staying at Margate for the month he spent most of the rest of his leave at Lausanne where he underwent treatment by Dr. Roger Vittoz at a clinic there. At Lausanne Eliot completed writing the draft of The Waste Land.
Source for mandoline information: Seymour-Jones, pp. 532-3