Attorney John Eastman gestures as he speaks next to U.S. President Donald Trump's personal attorney Rudy Giuliani, as Trum...

Who is John Eastman and why is he important to the Jan. 6 hearings?

While it is unlikely that conservative lawyer John Eastman will testify publicly before the Jan. 6 committee, his name and the legal advice he gave former President Donald Trump was raised repeatedly during the June 16 hearing focused on former Vice President Mike Pence.

WATCH: Jan. 6 committee hearings – Day 3

Eastman, a founding director of the Center for Constitutional Jurisprudence, a law firm that is part of the conservative think tank The Claremont Institute, gave the president legal advice after he lost the 2020 election. He was critical to perpetuating the myth that there were legal pathways to overturn the results. In December, he filed a brief on Trump’s behalf in a Texas lawsuit challenging Biden’s win before the Supreme Court. The court threw the case out, but Eastman kept up his efforts.

In late 2020, he wrote and circulated a series of memos espousing the theory that the vice president is “the ultimate arbiter” of the election and had the power to delay Congress’ count of Electoral College votes.

During the June 16 hearing, Pence lawyer Greg Jacob and retired conservative Judge J. Michael Luttig repeatedly dismantled Eastman’s theory that the vice president has the constitutional authority to reject states’ slates of electors or delay the certification of votes at all.

Jacob explained that in the days leading up to Jan. 6, Eastman presented two paths for how Pence could keep Trump in power. He could outright reject the electors and their votes or he could delay the certification for 10 days, which would give state legislatures time to send Trump-friendly electors for a later vote count.

Both Jacob and Luttig testified before the committee that both avenues were illegal, and Jacob said Pence never considered either option. Aguilar also showed an October memo in which Eastman himself noted that those pathways were not legal.

Jacob testified that Eastman switched back and forth over which route he recommended, noting that the second might be more “politically palatable,” and insisted the 10 days would be time to get public acceptance for the move.

Despite Pence never entertaining Eastman’s suggestions, Eastman pushed the issue numerous times up through Jan. 6.

Eastman spoke alongside Trump lawyer Rudy Giuliani at Trump’s Jan. 6 rally before rioters headed toward the Capitol. During the siege, he exchanged emails with Jacob.

“The ‘siege’ is because YOU and your boss did not do what was necessary to allow this to be aired in a public way so that the American people can see for themselves what happened,” Eastman wrote to Jacob.

After the insurrection, which delayed the count beyond what is technically called for in the Electoral Count Act, Eastman tried at least once more to convince the vice president to delay the certification.

“Now that we have established that the Electoral Count Act is not so sacrosanct as you have made it out to be, I implore you to consider one more relatively minor violation and adjourn for 10 days to allow the legislatures to finish their investigations,” he emailed Pence.

Days later, Eastman emailed Trump lawyer Rudy Giuliani asking to be placed on a potential presidential pardon list, the committee revealed, though he ultimately was not.

As a result of his heavy involvement in the post-election efforts to keep Trump in the presidency, the committee subpoenaed Eastman in the course of its investigation, and he testified in closed-door interviews. However, he invoked 5th Amendment protections against self-incrimination for 100 questions, committee Rep. Pete Aguilar, D-Calif., said at the June 16 hearing.

He also initially refused to turn over a trove of documents the committee requested. He released them after a judge ordered him to do so.

On Wednesday, the Washington Post reported that Eastman had also exchanged emails about tactics to overturn the election with conservative activist Ginni Thomas, who is also the wife of Supreme Court Justice Clarence Thomas. Eastman previously clerked for Justice Thomas.

For more on the key players in the Jan. 6 committee hearings, click here.