Gaelic and Basque are not related except in the sense that most human languages are related. Gaelic is a member of the Indo-European group, while Basque is not; it is generally considered by linguists to be a unique neolithic survival.

Recent reports of genetic links between people in the Basque country and people in Wales have frequently been misunderstood by subscribers to the relatively modern romantic notions of the 'pan Celticists' as indicating that the Basques are Celts. In fact, the reverse is indicated: that the Welsh, on the whole, are not, genetically speaking, 'Celts' at all, but descendants of the aboriginal inhabitants of Western Europe who were here long before the historical Celts arrived.

Recent studies seem to suggest that the same is true of many of the people living in Ireland, Scotland and England today. The pre-Celts of the British Isles appear to have adopted Celtic languages and much of the culture without absorbing a particularly large genetic input. The Basques, perhaps for geographical reasons, retained their original language.

This has been fairly obvious to linguists for quite a long time, but it's only now that genetics seem to be confirming that we have been labouring under some pretty big historical misapprehensions for a good few centuries.

Interesting times.