"But if you ask why is anyone celebrating, no one knows. And then you get some people who say it shouldn't be celebrated at all because it's a foreign holiday -- and yet it's as American a holiday as the Fourth of July," he said.
"No one has seemed to link it to the Civil War," he added about what he called groundbreaking research.
UCLA history professor Stephen Aron said Hayes-Bautista's finding is significant.
"For the general public (and even for many historians), the California origins of the Cinco de Mayo holiday come as quite a surprise (since the holiday is so generally presumed to be a Mexican holiday that was only recently imported into the United States)," Aron said in an e-mail to CNN. "That Hayes-Bautista's book ties these origins to the American Civil War is also of great significance."
Rounding out the new research into Cinco de Mayo is Hayes-Bautista's family legend that recounts how his great-great-grandfather Bartolo Bautista was part of local militia supporting the Mexican army in the Battle of Puebla.
His ancestor, who hailed from the town of San Miguel de Atlautla just below the snow line on the volcano Popocatepetl, was taken prisoner but was spared execution by a French army firing squad after it saw he had a birthmark over his heart.
The mark was in the shape of a hand with all five fingers clearly visible, Hayes-Bautista said. The French firing squad had told the prisoners to remove their shirts because the soldiers intended to use the clothing.
Superstitious of the birth mark, the French let the man go, Hayes-Bautista said.
On Saturday, 150 years later, Hayes-Bautista is scheduled to participate in a Cinco de Mayo celebration at LA Plaza de Cultura y Artes, a Smithsonian affiliate in downtown Los Angeles.