The language of the money shot (for our purposes) in the 12th Amendment is peculiar. PAUSE I can't believe I am reading the fucking 12th Amendment UNPAUSE:

“The President of the Senate shall, in the presence of the Senate and House of Representatives, open all the certificates and the votes shall then be counted;”

Active voice: “President of the Senate SHALL...OPEN...”

Then passive voice: “and the votes SHALL THEN BE COUNTED."

Who? Who counts once Pence opens.

It specifically does NOT say the votes shall be counted by the PRESIDENT of the Senate. 

The 12th A. gives no active role to the President of the Senate besides opening.

The practice seemingly countenanced there is that of the reception of jury verdicts. Judge “opens”, checks that it’s signed by foreperson (in the present case, that the states' electoral votes are under seal of the states) and then the clerk reads the verdict and polls each juror individually. 

Some anti-democratic elected representatives have filed suit against Pence. The suit asks SCOTUS to declare that the President of the Senate is the sole counter of the electoral votes and the sole determiner of the election winner. The 12th A. doesn’t say that.

*Updated. Gohmert's claim conflicts with legal experts who say that Pence’s role, or the role of any vice president, is to preside over the counting of the votes submitted by the Electoral College, not to judge which ones are valid or not.

Just as a judge does upon receipt of a jury verdict. A judge cannot override a jury verdict.