The Constitution establishes no other role for the Electors than to vote for the president. Your suggestion that they are to determine eligibility is pure speculation and there is no historical precedent for the electors ever performing that function.
It is Congress who can stop an ineligible candidate by refusing to certify his/her Electors or count the Electoral votes from any particular state.
Today, 21 states allow electors to not necessarily vote for the winner of the state’s popular vote (”faithless electors”). Electors in those 21 states could eadily deny any candidate the necessary 270 electoral votes that are required.
Correct.
However, to me at least it is obvious the Founders intended the EC to be composed of men who would actually between them decide who should be the next president. There is not a hint in the Constitution of the states being intended to instruct the electors who they should vote for.
This can be seen in what Hamilton wrote in Federalist 68:
It was equally desirable, that the immediate election should be made by men most capable of analyzing the qualities adapted to the station, and acting under circumstances favorable to deliberation, and to a judicious combination of all the reasons and inducements which were proper to govern their choice. A small number of persons, selected by their fellow-citizens from the general mass, will be most likely to possess the information and discernment requisite to such complicated investigations.
That sure sounds to me like the Electors were expected to use their judgment as to whether the candidates met the constitutional requirements.
Many constitutional scholars think the Founders expected the electors to routinely split their vote many ways, hence the unusually detailed procedures for Congress to decide among the leaders in the EC.
The Constitution never really functioned in this way. Washington was elected by acclamation twice, and by the third election party politics had already emerged and the EC never did function as an actual electoral body.