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• 1 11 12 no additional effect (only if Favoured by the ..., but since due to the rules this doesn’t grant a Piercing Blow, the 1 here is just converted to a 2 only)

• 1-6 2-7 no additional effect

• 7 8 Piercing Blow (but only with the dwarvish SUPERIOR KEEN reward, otherwise: no additional effect)

• 8 9 Piercing Blow (but only with the KEEN reward, otherwise: no additional effect)

• 9 10 Piercing Blow

• 10 11 Piercing Blow (since the result is capped at 10, so no disadvantage due to being Dour-handed)

• Gandalf rune Gandalf appears, turns into his White embodiment and all enemies are suddenly “Blinded by the light” https://www.youtube.com/watch?v=Rpq35wyDi7I !

Your math looks right to me. However...

I think calling the Eye of Sauron rune an "11" causes a lot of confusion. There is no such thing as an 11 or 12 on a TOR feat die. It's a d10 with two extra possible results that aren't numbers at all. I've heard a lot of people do this in videos and forums, and I understand why they do. I just think it muddies the waters.

I think calling the Eye of Sauron rune an "11" causes a lot of confusion.

The 12-sided effect die may yield numerical values from 0 to 10 (only, and 0 can only be the result of an effect that reduces the die result – barring that, the value range is 1 to 10). The eye and Gandalf rune are not equal to the numerical values 11/12, they just take the place of those numbers on an ordinary W12. They are triggers for certain effects, not particularly good/bad numbers. This means that an effect that adds 1 to your effect die can raise a 9 to a 10, but never a 10 to an Eye nor an Eye to a Gandalf. Numerical values are capped at 10, you cannot have a result higher than 10. A "10 + 1" is a 10, basta.
Concerning piercing damage, the value 10 (and the 9, if your weapon is keen) is also just a trigger for that kind of damage, but in this case it means the end result of the die. If some effect raises your W12 result from 9 to 10, it is a 10 and thus, for example, triggers "piercing".
If you roll an Eye in any Test, the W12 simply does not count for the end result (ignore the rule sentence that say it is "0", this is rubbish). (If you are Miserable, it even triggers an automatic and unconditional failure.)

Lol. Oh yeah. Forgot about those guys. (I still can't believe those dice got away from Free League like that.) But also anyone using a regular d12. (Lucky for me I have my dice from 1e.) Like I say, I get why people say it. But the system doesn't work right if you think of it that way. If you add +1 to an Eye of Sauron you don't get a Gandalf Rune. Stuff like that.

When explaining the 12-sided die to the players, would it be correct to say this?

The 12-sided effect die may yield numerical values from 0 to 10 (only, and 0 can only be the result of an effect that reduces the die result – barring that, the value range is 1 to 10). The eye and Gandalf rune are not equal to the numerical values 11/12, they just take the place of those numbers on an ordinary W12. They are triggers for certain effects, not particularly good/bad numbers. This means that an effect that adds 1 to your effect die can raise a 9 to a 10, but never a 10 to an Eye nor an Eye to a Gandalf. Numerical values are capped at 10, you cannot have a result higher than 10. A "10 + 1" is a 10, basta.
Concerning piercing damage, the value 10 (and the 9, if your weapon is keen) is also just a trigger for that kind of damage, but in this case it means the end result of the die. If some effect raises your W12 result from 9 to 10, it is a 10 and thus, for example, triggers "piercing".
If you roll an Eye in any Test, the W12 simply does not count for the end result (ignore the rule sentence that say it is "0", this is rubbish). (If you are Miserable, it even triggers an automatic and unconditional failure.)

Is it because you can increase a 0 in theory which isn’t what the Eye is meant for?