re: Should Illegal Aliens count towards congressional representation?

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This is clearly stating that if there are persons in the count that aren’t eligible to vote (for reasons other than age, insurrection, or being a criminal) then that State’s representation should be reduced by a proportional amount.

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No. It's the complete opposite. It's stating that if a state deny's a person a write to vote, except for "participation in rebellion, or other crime," then the state's appropriation will be minimized.

It's never been successfully enforced, but it's intent was to prevent state's from denying disenfranchised voters (e.g., African-Americans) the right to vote. Here is an article about it:

Right to Vote and Judicial Enforcement of Section Two of the Fourteenth Amendment

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Particularly noteworthy of this first attempt at solving the representational problem posed by the newly emancipated Negro, was the provision for reduction of a state's representation solely when that state denied or abridged the right to vote for reasons of race.

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