He received a Bachelor of Business Administration degree from the University of Arkansas at Fayetteville and joined the insurance agency owned by his father in Little Rock.
[3] In the spring of 1970, however, Cockrill switched affiliation to the Republican Party to run for lieutenant governor on the GOP ticket headed by the two-term Rockefeller, who sought a third-term in office.
"[4] Cockrill won the Republican nomination for lieutenant governor with 88 percent of the vote over the politically unknown Gerald Williams of North Little Rock.
[3] Though they waged vigorous campaigns, Rockefeller and Cockrill were defeated by the united Democratic slate headed by Dale Bumpers and Bob C. Riley.
The remaining 4 percent of the vote was cast for the American Independent Party nominee Hubert Blanton of Hughes in St. Francis County.
[6] Riley attributed his victory to the Democratic "team effort" and accused Cockrill of having engaged in "mudslinging, character assassination, and hate emotions".