A google search for cocteau twins tranquil eye lyrics returns links to dozens of song-lyrics sites. All of the lyrics-site links I followed returned “no lyrics for this song” (or equivalent) messages.
More positively, some of the links led to statements about or analyses of lyrics of Cocteau Twins songs (1,2,3). It appears that many of the words in their songs are English, and many are not; and the English words often don't form sentences. It's easy to hear numerous English words scattered through the Tranquil Eye youtube that you linked to. As another example, the first chorus of Violaine is:
Ik does a dashik dozen
Ik does a yield gig does
Ik does alone Cheyenne
Mad at them who tease him scrawling
which includes a mix of Dutch or German-like words with a good bit of English.