Excuse me, please, just an observation. The verb: To go ( translated into Gaelic by Téann tu ), belongs to the second or first conjugation? I see that the final part, in the sentence, is written as: Téann tú, is added -ann to the final part, when is cutted -igh, from téigh, and that means Teigh belongs to the first conjugation, and not to the second conjugation. Or not?
"To go" or "Téigh" is one of the few irregular verbs in Irish: https://en.wikipedia.org/wiki/Irish_conjugation#t.C3.A9igh_.22to_go.22
The purpose of the leathan le leathan, caol le caol rule is to align the vowels on either side of a consonant. There is no rule that requires the vowel next to a vowel agree, because that would prevent ae, ai, ea, eo, ia, etc, etc ever occurring. As é is what makes the T slender, and there is no need for the é to agree with the following vowel, there is no need to choose the "slender" eann ending, particularly as it would mean that téann would be spelled téeann, and that middle e* would serve no purpose, and Irish doesn't use double vowels.