This is how you object to an illegal or ineligible President -Elect:
3 US Code § 15
Congress shall be in session on the sixth day of January succeeding every meeting of the electors. The Senate and House of Representatives shall meet in the Hall of the House of Representatives at the hour of 1 o’clock in the afternoon on that day, and the President of the Senate shall be their presiding officer. Two tellers shall be previously appointed on the part of the Senate and two on the part of the House of Representatives, to whom shall be handed, as they are opened by the President of the Senate, all the certificates and papers purporting to be certificates of the electoral votes, which certificates and papers shall be opened, presented, and acted upon in the alphabetical order of the States, beginning with the letter A; and said tellers, having then read the same in the presence and hearing of the two Houses, shall make a list of the votes as they shall appear from the said certificates; and the votes having been ascertained and counted according to the rules in this subchapter provided, the result of the same shall be delivered to the President of the Senate, who shall thereupon announce the state of the vote, which announcement shall be deemed a sufficient declaration of the persons, if any, elected President and Vice President of the United States, and, together with a list of the votes, be entered on the Journals of the two Houses. Upon such reading of any such certificate or paper, the President of the Senate SHALL FOR OBJECTIONS, if any. Every OBJECTION shall be MADE IN WRITING, and shall state clearly and concisely, and without argument, the ground thereof, and shall be signed by at least one Senator and one Member of the House of Representatives before the same shall be received. When all objections so made to any vote or paper from a State shall have been received and read, the Senate shall thereupon withdraw, and such objections shall be submitted to the Senate for its decision; and the Speaker of the House of Representatives shall, in like manner, submit such objections to the House of Representatives for its decision; and no electoral vote or votes from any State which shall have been regularly given by electors whose appointment has been lawfully certified to according to section 6 of this title from which but one return has been received shall be rejected, but the two Houses concurrently may reject the vote or votes when they agree that such vote or votes have not been so regularly given by electors whose appointment has been so certified. If more than one return or paper purporting to be a return from a State shall have been received by the President of the Senate, those votes, and those only, shall be counted which shall have been regularly given by the electors who are shown by the determination mentioned in section 5 of this title to have been appointed, if the determination in said section provided for shall have been made, or by such successors or substitutes, in case of a vacancy in the board of electors so ascertained, as have been appointed to fill such vacancy in the mode provided by the laws of the State; but in case there shall arise the question which of two or more of such State authorities determining what electors have been appointed, as mentioned in section 5 of this title, is the lawful tribunal of such State, the votes regularly given of those electors, and those only, of such State shall be counted whose title as electors the two Houses, acting separately, shall concurrently decide is supported by the decision of such State so authorized by its law; and in such case of more than one return or paper purporting to be a return from a State, if there shall have been no such determination of the question in the State aforesaid, then those votes, and those only, shall be counted which the two Houses shall concurrently decide were cast by lawful electors appointed in accordance with the laws of the State, unless the two Houses, acting separately, shall concurrently decide such votes not to be the lawful votes of the legally appointed electors of such State. But if the two Houses shall disagree in respect of the counting of such votes, then, and in that case, the votes of the electors whose appointment shall have been certified by the executive of the State, under the seal thereof, shall be counted. When the two Houses have voted, they shall immediately again meet, and the presiding officer shall then announce the decision of the questions submitted. No votes or papers from any other State shall be acted upon until the objections previously made to the votes or papers from any State shall have been finally disposed of.
It’s not illegal to vote for an ineligible President. The US Constitution was developed after a delegation of some of the sovereignty that was gifted to the people and the states by God. God did not bestow sovereignty upon the US Constitution or Congress or the Supreme Court. The people and the states delegated sovereignty, immunities and privileges to the US federal government and may cancel the delegation of authority by electing an ineligible President.
The Eligibility Clause is not used to prevent the will of the people. The Eligibility Clause is used to determine if the people have cancelled the delegation of authority granted to the US federal government by the American people.
Review the Noel Canning Apppointments Clause challenge in the courts against the NRLB. The courts ruled Obama violated the Appointments Clause. Obama wasn’t removed from office for violating the Constitution. Obama was put in office by the will of the people. The courts are not authorized to terminate the will of the people. The courts are authorized to terminate the appointments made in violation of the Appointments Clause and rule all of the actions by those appointees are voided.
With a violation of the Eligibility Clause, the ineligible President is not removed. The courts and the Congress are servants of the people. The appointments, bills signed into law, and all others actions of the ineligible President are voided because the people have voted to install an ineligible President and move forward with new, national governing decree.