During the first meeting of the Senate in 2021, a Senate Concurrent Resolution will be proposed by unanimous consent. Following is the resolution from January 3, 2017. The responsibility of the President of the Senate, with respect to certificates, is shown emboldened.
S. CON. RES. 2
Resolved by the Senate (the House of Representatives concurring), That the two Houses of Congress shall meet in the Hall of the House of Representatives on Friday, the 6th day of January 2017, at 1 o’clock post meridian, pursuant to the requirements of the Constitution and laws relating to the election of President and Vice President of the United States, and the President of the Senate shall be their Presiding Officer; that two tellers shall be previously appointed by the President of the Senate on the part of the Senate and two by the Speaker 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 said certificates; and the votes having been ascertained and counted in the manner and according to the rules by law 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.
After the Senate approves the resolution, the House concurs; thus providing for the January 6th joint session. On January 6th, the joint session is held pursuant to the resolution.
Assuming a resolution with the same wording, the President of the Senate is required to open "all the certificates and papers purporting to be certificates of the electoral votes, ...". Furthermore, because any objections to the certificate of any state must be made in writing and signed before the counting of any votes, Senators and Representatives are aware of which certificates are to be opened and their sequence. Any deviation from the required and known sequence would give rise to an objection. There is no rule nor procedure to resolve the objection; therefore, no apparent means to continue with the count until the proper certificates have been opened and read.
Can the Vice President ignore electors or is he just more of a figure ''Image'' and has no real authority?
It is more ceremonial, than anything else. Just as having the Speaker sit next to the President of the Senate during the count is ceremonial.
What's the procedure if he were to refuse?
The is no apparent procedure beyond the possible objection and delay as mentioned above.
Is there a secondary (Secretary, etc..) who it goes to?