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This is an interesting story.
Actually, the Tocharians themselves remain pretty hard to place exactly. The odd thing about Tocharian is that as an Indo-European language it is geographically displaced from languages within its own linguistic division (i.e. other Centum languages). Indo-European languages are divided into Centum and Satem language groups, the word for one hundred (100) in Latin and Sanskrit respectively. Roughly speaking, Centum languages are found in Western Europe and Satem languages are found in Eastern Europe, Iran, and Northern India. Tocharian was generally spoken to the north and east of Iran in Central Asia.
One clue alluded to here concerning who the Tocharians might have been was uncovered (literally) early at the beginning of the last century when a cache of mummies was discovered in the Tarim Basin in western China. The mummies had been preserved as a result of the arid climate conditions.
Initially, the discoverers were stumped as to what to make of them. They were surprised to find that these mummies were apparently (verified subsequently) the bodies of an ancient (1800 BCE) Western European-related people. Humans depicted on frescoes found in the general vicinity were also mostly Western-European in appearance. Mummies with red and blond hair were found. From thence comes the allusion to the Irish.
There's an interesting book that covers not only issues surrounding the "mystery" of the Tocharians both genetically and linguistically (and in many other ways), but also details the history of the excavations as well.
The book is "The Tarim Mummies" by J. P. Mallory and Victor H. Mair, Thames & Hudson, Ltd., London 2000.