Representatives shall be apportioned among the several states according to their respective numbers, counting the whole number of persons in each state, excluding Indians not taxed. But when the right to vote at any election for the choice of electors for President and Vice President of the United States, Representatives in Congress, the executive and judicial officers of a state, or the members of the legislature thereof, is denied to any of the male inhabitants of such state, being twenty-one years of age, and citizens of the United States, or in any way abridged, except for participation in rebellion, or other crime, the basis of representation therein shall be reduced in the proportion which the number of such male citizens shall bear to the whole number of male citizens twenty-one years of age in such state.
The point is reinforced, that representation should only be apportioned (i.e. allocated) based on the citizen population of the states.
The 14th Amendment was all about citizenship and primarily added to the Constitution to make sure black males born in the country were recognized, and counted (i.e. "WHOLE") as a citizen. Why does the 14th Amendment use the word "whole" more than once? Because the original Constitution counted blacks as 3/5's a person [1], which was done primarily to prevent the south from having even more power (i.e. Representatives in the House). Imagine how difficult it would have been to eventually eliminate slavery if the south had more political power during those years!
Since the 14th Amendment, the 19th Amendment was passed to allow women to vote in state and federal elections (they could already vote in some local elections much earlier) [2]
This is indeed proof that if a census is to be used to apportion, or determine the number of, House of Reps by state, that citizenship is the qualifier and therefore must be included on any census in order to justify the number of Reps based on number of citizens.
As you pointed out in the lower portion of your post, I removed the words "male" due to the 19th amendment obviating them. I didn't want them to obscure the point being made, which is that section 2 was about counting citizens for representation purposes, not just "persons."
-PJ